Twee---2.7.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : LCL256-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n026.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Sep 29 11:49:30 AM UTC 2026

% Result   : Unsatisfiable 34.72s 4.89s
% Output   : Proof 89.05s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : LCL256-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04  % Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37  % Computer : n026.cluster.edu
% 0.11/0.37  % Model    : x86_64 x86_64
% 0.11/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37  % Memory   : 8046.5625MB
% 0.11/0.37  % OS       : Linux 6.8.0-71-generic
% 0.11/0.37  % CPULimit : 300
% 0.11/0.37  % WCLimit  : 300
% 0.11/0.37  % DateTime : Sun Sep 27 15:34:11 UTC 2026
% 0.11/0.37  % CPUTime  : 
% 0.11/0.37  Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 34.72/4.89  Command-line arguments: --no-flatten-goal
% 34.72/4.89  
% 34.72/4.89  % SZS status Unsatisfiable
% 34.72/4.89  
% 67.23/10.11  % SZS output start Proof
% 67.23/10.11  Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 67.23/10.11  Axiom 2 (cn_3): is_a_theorem(implies(X, implies(not(X), Y))) = true.
% 67.23/10.11  Axiom 3 (cn_2): is_a_theorem(implies(implies(not(X), X), X)) = true.
% 67.23/10.11  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.
% 67.94/10.22  Axiom 5 (cn_1): is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true.
% 67.94/10.22  
% 67.94/10.22  Goal 1 (prove_not_not_implies): is_a_theorem(not(not(implies(p, p)))) = true.
% 67.94/10.22  Proof:
% 67.94/10.22    is_a_theorem(not(not(implies(p, p))))
% 67.94/10.22  = { by axiom 1 (ifeq_axiom) R->L }
% 67.94/10.22    ifeq(true, true, is_a_theorem(not(not(implies(p, p)))), true)
% 67.94/10.22  = { by axiom 4 (condensed_detachment) R->L }
% 67.94/10.23    ifeq(ifeq(is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true, ifeq(is_a_theorem(implies(not(implies(p, p)), not(implies(p, p)))), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 67.94/10.23  = { by axiom 1 (ifeq_axiom) R->L }
% 67.94/10.23    ifeq(ifeq(is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(p, p)), not(implies(p, p)))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 67.94/10.23  = { by axiom 4 (condensed_detachment) R->L }
% 67.94/10.23    ifeq(ifeq(is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(p, p)), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(not(implies(p, p)), not(implies(p, p)))))), true, ifeq(is_a_theorem(implies(not(implies(p, p)), implies(not(not(implies(p, p))), not(implies(p, p))))), true, is_a_theorem(implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(not(implies(p, p)), not(implies(p, p))))), true), true), true, is_a_theorem(implies(not(implies(p, p)), not(implies(p, p)))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 67.94/10.23  = { by axiom 2 (cn_3) }
% 67.94/10.23    ifeq(ifeq(is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(p, p)), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(not(implies(p, p)), not(implies(p, p)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(not(implies(p, p)), not(implies(p, p))))), true), true), true, is_a_theorem(implies(not(implies(p, p)), not(implies(p, p)))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 67.94/10.23  = { by axiom 1 (ifeq_axiom) }
% 67.94/10.23    ifeq(ifeq(is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(p, p)), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(not(implies(p, p)), not(implies(p, p)))))), true, is_a_theorem(implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(not(implies(p, p)), not(implies(p, p))))), true), true, is_a_theorem(implies(not(implies(p, p)), not(implies(p, p)))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 67.94/10.23  = { by axiom 5 (cn_1) }
% 67.94/10.24    ifeq(ifeq(is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(not(implies(p, p)), not(implies(p, p))))), true), true, is_a_theorem(implies(not(implies(p, p)), not(implies(p, p)))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 67.94/10.24  = { by axiom 1 (ifeq_axiom) }
% 67.94/10.24    ifeq(ifeq(is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(not(implies(p, p)), not(implies(p, p))))), true, is_a_theorem(implies(not(implies(p, p)), not(implies(p, p)))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 67.94/10.24  = { by axiom 1 (ifeq_axiom) R->L }
% 67.94/10.24    ifeq(ifeq(is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(not(implies(p, p)), not(implies(p, p))))), true, ifeq(true, true, is_a_theorem(implies(not(implies(p, p)), not(implies(p, p)))), true), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 67.94/10.24  = { by axiom 3 (cn_2) R->L }
% 67.94/10.24    ifeq(ifeq(is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(not(implies(p, p)), not(implies(p, p))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p)))), true, is_a_theorem(implies(not(implies(p, p)), not(implies(p, p)))), true), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 67.94/10.24  = { by axiom 4 (condensed_detachment) }
% 67.94/10.24    ifeq(ifeq(is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true, ifeq(true, true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 67.94/10.24  = { by axiom 1 (ifeq_axiom) }
% 67.94/10.24    ifeq(ifeq(is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 67.94/10.24  = { by axiom 1 (ifeq_axiom) R->L }
% 67.94/10.24    ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 67.94/10.25  = { by axiom 4 (condensed_detachment) R->L }
% 67.94/10.25    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p)))))), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 67.94/10.25  = { by axiom 1 (ifeq_axiom) R->L }
% 67.94/10.25    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p)))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 67.94/10.25  = { by axiom 5 (cn_1) R->L }
% 67.94/10.25    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(implies(p, p)))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p)))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 67.94/10.25  = { by axiom 1 (ifeq_axiom) R->L }
% 67.94/10.26    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(implies(p, p)))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p)))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 67.94/10.26  = { by axiom 2 (cn_3) R->L }
% 67.94/10.26    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(implies(p, p)))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))))), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p)))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 67.94/10.26  = { by axiom 4 (condensed_detachment) }
% 67.94/10.26    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 67.94/10.26  = { by axiom 1 (ifeq_axiom) }
% 67.94/10.26    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 67.94/10.27  = { by axiom 1 (ifeq_axiom) R->L }
% 67.94/10.27    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 67.94/10.27  = { by axiom 4 (condensed_detachment) R->L }
% 67.94/10.27    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 67.94/10.28  = { by axiom 1 (ifeq_axiom) R->L }
% 67.94/10.28    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 67.94/10.29  = { by axiom 4 (condensed_detachment) R->L }
% 67.94/10.29    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(implies(p, p))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(not(not(implies(p, p))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 68.65/10.30  = { by axiom 1 (ifeq_axiom) R->L }
% 68.65/10.31    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(implies(p, p))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(not(not(implies(p, p))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 68.65/10.31  = { by axiom 5 (cn_1) R->L }
% 68.65/10.32    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(implies(not(not(not(implies(p, p)))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(implies(p, p))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(implies(p, p))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(not(not(implies(p, p))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 68.65/10.32  = { by axiom 1 (ifeq_axiom) R->L }
% 68.65/10.33    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(implies(not(not(not(implies(p, p)))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(implies(p, p))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(implies(p, p))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(not(not(implies(p, p))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 68.65/10.33  = { by axiom 2 (cn_3) R->L }
% 68.65/10.34    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(implies(not(not(not(implies(p, p)))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(implies(p, p))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true, ifeq(is_a_theorem(implies(not(not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(implies(p, p))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(not(not(implies(p, p))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 68.65/10.34  = { by axiom 4 (condensed_detachment) }
% 68.65/10.34    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(not(not(implies(p, p))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 68.65/10.35  = { by axiom 1 (ifeq_axiom) }
% 68.65/10.35    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(not(not(implies(p, p))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 68.65/10.36  = { by axiom 1 (ifeq_axiom) R->L }
% 68.65/10.36    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 68.65/10.37  = { by axiom 5 (cn_1) R->L }
% 68.65/10.37    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(implies(not(not(not(implies(p, p)))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 68.65/10.37  = { by axiom 1 (ifeq_axiom) R->L }
% 68.65/10.38    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(implies(not(not(not(implies(p, p)))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(not(not(implies(p, p))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 68.65/10.38  = { by axiom 3 (cn_2) R->L }
% 68.65/10.39    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(implies(not(not(not(implies(p, p)))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(not(not(implies(p, p))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 68.65/10.39  = { by axiom 4 (condensed_detachment) }
% 68.65/10.39    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(implies(p, p))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 68.65/10.39  = { by axiom 1 (ifeq_axiom) }
% 68.65/10.40    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(not(implies(p, p))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 69.36/10.40  = { by axiom 1 (ifeq_axiom) R->L }
% 69.36/10.40    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(not(implies(p, p))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 69.36/10.40  = { by axiom 5 (cn_1) R->L }
% 69.36/10.41    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(p, p))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true, ifeq(is_a_theorem(implies(not(not(implies(p, p))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 69.36/10.41  = { by axiom 4 (condensed_detachment) }
% 69.36/10.41    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 69.36/10.42  = { by axiom 1 (ifeq_axiom) }
% 69.36/10.42    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 69.36/10.42  = { by axiom 1 (ifeq_axiom) R->L }
% 69.36/10.43    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 69.36/10.44  = { by axiom 4 (condensed_detachment) R->L }
% 69.36/10.44    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 69.36/10.45  = { by axiom 1 (ifeq_axiom) R->L }
% 69.36/10.46    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 69.36/10.47  = { by axiom 4 (condensed_detachment) R->L }
% 69.36/10.48    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 69.36/10.49  = { by axiom 5 (cn_1) }
% 70.06/10.50    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 70.06/10.52  = { by axiom 1 (ifeq_axiom) }
% 70.06/10.53    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 70.06/10.54  = { by axiom 1 (ifeq_axiom) R->L }
% 70.06/10.55    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 70.06/10.56  = { by axiom 5 (cn_1) R->L }
% 70.06/10.58    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 70.06/10.59  = { by axiom 1 (ifeq_axiom) R->L }
% 70.06/10.59    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 70.76/10.60  = { by axiom 3 (cn_2) R->L }
% 70.76/10.61    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 70.76/10.63  = { by axiom 4 (condensed_detachment) }
% 70.76/10.63    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 70.76/10.66  = { by axiom 1 (ifeq_axiom) }
% 70.76/10.67    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 70.76/10.68  = { by axiom 1 (ifeq_axiom) R->L }
% 70.76/10.69    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 70.76/10.71  = { by axiom 4 (condensed_detachment) R->L }
% 70.76/10.73    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 70.76/10.74  = { by axiom 5 (cn_1) }
% 71.81/10.76    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 71.81/10.77  = { by axiom 1 (ifeq_axiom) }
% 71.81/10.78    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 71.81/10.79  = { by axiom 5 (cn_1) }
% 71.81/10.80    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(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 71.81/10.81  = { by axiom 1 (ifeq_axiom) }
% 71.81/10.82    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 71.81/10.82  = { by axiom 4 (condensed_detachment) }
% 71.81/10.83    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 71.81/10.83  = { by axiom 1 (ifeq_axiom) }
% 71.81/10.84    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 71.81/10.84  = { by axiom 1 (ifeq_axiom) R->L }
% 71.81/10.85    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 71.81/10.85  = { by axiom 4 (condensed_detachment) R->L }
% 72.58/10.86    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true, ifeq(is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 72.58/10.87  = { by axiom 5 (cn_1) }
% 72.58/10.88    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 72.58/10.89  = { by axiom 1 (ifeq_axiom) }
% 72.58/10.89    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 72.89/10.90  = { by axiom 1 (ifeq_axiom) R->L }
% 72.89/10.91    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 72.89/10.92  = { by axiom 4 (condensed_detachment) R->L }
% 72.89/10.93    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(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 72.89/10.95  = { by axiom 1 (ifeq_axiom) R->L }
% 72.89/10.96    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(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 72.89/10.97  = { by axiom 5 (cn_1) R->L }
% 72.89/10.98    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 72.89/10.99  = { by axiom 1 (ifeq_axiom) R->L }
% 73.57/11.00    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 73.57/11.01  = { by axiom 5 (cn_1) R->L }
% 73.57/11.02    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 73.57/11.03  = { by axiom 4 (condensed_detachment) }
% 73.57/11.04    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(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 73.57/11.05  = { by axiom 1 (ifeq_axiom) }
% 73.57/11.06    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(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 73.57/11.08  = { by axiom 1 (ifeq_axiom) R->L }
% 73.57/11.08    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(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 74.27/11.10  = { by axiom 4 (condensed_detachment) R->L }
% 74.27/11.11    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(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(not(not(implies(p, p))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p)))))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(not(not(implies(p, p))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))))), true, is_a_theorem(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 74.27/11.14  = { by axiom 1 (ifeq_axiom) R->L }
% 74.27/11.15    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(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(not(not(implies(p, p))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(not(not(implies(p, p))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))))), true, is_a_theorem(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 74.27/11.16  = { by axiom 5 (cn_1) R->L }
% 74.27/11.18    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(not(not(implies(p, p)))))), implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(not(not(implies(p, p))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(not(not(implies(p, p))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(not(not(implies(p, p))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))))), true, is_a_theorem(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 74.27/11.19  = { by axiom 1 (ifeq_axiom) R->L }
% 74.97/11.20    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(not(not(implies(p, p)))))), implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(not(not(implies(p, p))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(not(not(implies(p, p))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(not(not(implies(p, p))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))))), true, is_a_theorem(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 74.97/11.21  = { by axiom 2 (cn_3) R->L }
% 74.97/11.22    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(not(not(implies(p, p)))))), implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(not(not(implies(p, p))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))))))), true, ifeq(is_a_theorem(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(not(not(implies(p, p))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(not(not(implies(p, p))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(not(not(implies(p, p))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))))), true, is_a_theorem(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 74.97/11.24  = { by axiom 4 (condensed_detachment) }
% 74.97/11.25    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(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(not(not(implies(p, p))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))))), true, is_a_theorem(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 74.97/11.26  = { by axiom 1 (ifeq_axiom) }
% 74.97/11.27    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(not(not(implies(p, p))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))))), true, is_a_theorem(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 74.97/11.29  = { by axiom 1 (ifeq_axiom) R->L }
% 74.97/11.30    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(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(not(not(implies(p, p))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))))), true), true, is_a_theorem(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 75.68/11.31  = { by axiom 5 (cn_1) R->L }
% 75.68/11.32    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(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(not(not(implies(p, p))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(not(not(implies(p, p))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))))), true), true, is_a_theorem(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 75.68/11.33  = { by axiom 1 (ifeq_axiom) R->L }
% 75.68/11.34    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(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(not(not(implies(p, p))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(not(not(implies(p, p))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))))), true), true), true, is_a_theorem(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 75.68/11.35  = { by axiom 3 (cn_2) R->L }
% 75.68/11.36    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(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(not(not(implies(p, p))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p)))))))), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(not(not(implies(p, p))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))))), true), true), true, is_a_theorem(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 75.68/11.37  = { by axiom 4 (condensed_detachment) }
% 75.68/11.39    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 75.68/11.40  = { by axiom 1 (ifeq_axiom) }
% 76.39/11.41    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 76.39/11.41  = { by axiom 1 (ifeq_axiom) R->L }
% 76.39/11.42    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 76.39/11.43  = { by axiom 5 (cn_1) R->L }
% 76.39/11.44    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p)))))), implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, ifeq(is_a_theorem(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(implies(p, p))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 76.39/11.45  = { by axiom 4 (condensed_detachment) }
% 76.39/11.45    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 76.39/11.47  = { by axiom 1 (ifeq_axiom) }
% 76.39/11.47    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 76.39/11.48  = { by axiom 1 (ifeq_axiom) R->L }
% 76.39/11.49    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 77.09/11.50  = { by axiom 4 (condensed_detachment) R->L }
% 77.09/11.51    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true, ifeq(is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 77.09/11.52  = { by axiom 5 (cn_1) }
% 77.09/11.53    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 77.09/11.55  = { by axiom 1 (ifeq_axiom) }
% 77.09/11.56    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 77.09/11.58  = { by axiom 1 (ifeq_axiom) R->L }
% 77.09/11.59    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 77.80/11.60  = { by axiom 4 (condensed_detachment) R->L }
% 77.80/11.62    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), implies(implies(implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))))), true, ifeq(is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 77.80/11.64  = { by axiom 5 (cn_1) }
% 77.80/11.65    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(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 77.80/11.67  = { by axiom 1 (ifeq_axiom) }
% 77.80/11.68    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 77.80/11.70  = { by axiom 1 (ifeq_axiom) R->L }
% 77.80/11.71    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(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 77.80/11.75  = { by axiom 5 (cn_1) R->L }
% 78.86/11.77    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(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 78.86/11.80  = { by axiom 1 (ifeq_axiom) R->L }
% 78.86/11.82    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(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 78.86/11.84  = { by axiom 4 (condensed_detachment) R->L }
% 79.58/11.87    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(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(not(not(implies(p, p)))))))), implies(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))))), true, ifeq(is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 79.58/11.89  = { by axiom 2 (cn_3) }
% 79.91/11.91    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(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(not(not(implies(p, p)))))))), implies(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 79.91/11.93  = { by axiom 1 (ifeq_axiom) }
% 79.91/11.95    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(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(not(not(implies(p, p)))))))), implies(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 79.91/11.96  = { by axiom 5 (cn_1) }
% 79.91/11.98    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(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 80.61/12.00  = { by axiom 1 (ifeq_axiom) }
% 80.61/12.01    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(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))))), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 80.61/12.04  = { by axiom 4 (condensed_detachment) }
% 80.61/12.05    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(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 80.61/12.08  = { by axiom 1 (ifeq_axiom) }
% 80.61/12.09    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 81.32/12.12  = { by axiom 1 (ifeq_axiom) R->L }
% 81.32/12.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))))), true, ifeq(true, true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 81.32/12.15  = { by axiom 4 (condensed_detachment) R->L }
% 81.32/12.17    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))))), true, ifeq(is_a_theorem(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 81.32/12.19  = { by axiom 2 (cn_3) }
% 82.02/12.21    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 82.02/12.22  = { by axiom 1 (ifeq_axiom) }
% 82.02/12.24    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 82.02/12.25  = { by axiom 5 (cn_1) }
% 82.02/12.26    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 82.02/12.27  = { by axiom 1 (ifeq_axiom) }
% 82.02/12.28    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(not(implies(p, p)))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 82.02/12.29  = { by axiom 4 (condensed_detachment) }
% 82.02/12.30    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 82.73/12.30  = { by axiom 1 (ifeq_axiom) }
% 82.73/12.31    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), implies(not(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 82.73/12.32  = { by axiom 4 (condensed_detachment) }
% 82.73/12.32    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 82.73/12.33  = { by axiom 1 (ifeq_axiom) }
% 82.73/12.33    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 82.73/12.34  = { by axiom 1 (ifeq_axiom) R->L }
% 82.73/12.35    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 82.73/12.36  = { by axiom 4 (condensed_detachment) R->L }
% 82.73/12.37    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 82.73/12.38  = { by axiom 5 (cn_1) }
% 82.73/12.38    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 82.73/12.40  = { by axiom 1 (ifeq_axiom) }
% 83.43/12.40    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 83.43/12.42  = { by axiom 1 (ifeq_axiom) R->L }
% 83.43/12.42    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 83.43/12.43  = { by axiom 5 (cn_1) R->L }
% 83.43/12.44    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 83.43/12.45  = { by axiom 1 (ifeq_axiom) R->L }
% 83.43/12.46    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 83.43/12.47  = { by axiom 3 (cn_2) R->L }
% 83.43/12.48    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 83.43/12.48  = { by axiom 4 (condensed_detachment) }
% 83.43/12.48    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 83.43/12.49  = { by axiom 1 (ifeq_axiom) }
% 83.43/12.49    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 84.12/12.50  = { by axiom 4 (condensed_detachment) }
% 84.12/12.50    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 84.12/12.51  = { by axiom 1 (ifeq_axiom) }
% 84.12/12.51    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 84.12/12.52  = { by axiom 1 (ifeq_axiom) R->L }
% 84.12/12.52    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 84.12/12.53  = { by axiom 4 (condensed_detachment) R->L }
% 84.12/12.53    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 84.12/12.54  = { by axiom 3 (cn_2) }
% 84.12/12.54    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, ifeq(true, true, is_a_theorem(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 84.12/12.55  = { by axiom 1 (ifeq_axiom) }
% 84.12/12.55    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 84.12/12.56  = { by axiom 1 (ifeq_axiom) R->L }
% 84.12/12.57    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 84.12/12.58  = { by axiom 5 (cn_1) R->L }
% 84.12/12.58    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true, is_a_theorem(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 84.12/12.59  = { by axiom 1 (ifeq_axiom) R->L }
% 84.12/12.59    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 84.12/12.59  = { by axiom 2 (cn_3) R->L }
% 84.82/12.60    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))))), true, ifeq(is_a_theorem(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true), true), true, is_a_theorem(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 84.82/12.60  = { by axiom 4 (condensed_detachment) }
% 84.82/12.61    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 84.82/12.61  = { by axiom 1 (ifeq_axiom) }
% 84.82/12.61    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))))), true, ifeq(is_a_theorem(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 84.82/12.62  = { by axiom 4 (condensed_detachment) }
% 84.82/12.62    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 84.82/12.62  = { by axiom 1 (ifeq_axiom) }
% 84.82/12.62    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 84.82/12.63  = { by axiom 1 (ifeq_axiom) R->L }
% 84.82/12.63    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 84.82/12.64  = { by axiom 4 (condensed_detachment) R->L }
% 84.82/12.64    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(p, p))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), implies(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(p, p))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p)))))), true, is_a_theorem(implies(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p)))))), true), true), true, ifeq(is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 84.82/12.65  = { by axiom 1 (ifeq_axiom) R->L }
% 84.82/12.65    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(p, p))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), implies(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(p, p))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p)))))), true), true), true, ifeq(is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 84.82/12.66  = { by axiom 5 (cn_1) R->L }
% 84.82/12.66    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(p, p))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), implies(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(p, p)))), implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(p, p))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))))), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(p, p))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p)))))), true), true), true, ifeq(is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 84.82/12.67  = { by axiom 1 (ifeq_axiom) R->L }
% 84.82/12.67    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(p, p))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), implies(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(p, p)))), implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(p, p))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(p, p))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p)))))), true), true), true, ifeq(is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 84.82/12.67  = { by axiom 2 (cn_3) R->L }
% 84.82/12.68    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(p, p))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), implies(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(p, p)))), implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(p, p))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))))), true, ifeq(is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(p, p))))), true, is_a_theorem(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(p, p))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p)))))), true), true), true, ifeq(is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 84.82/12.68  = { by axiom 4 (condensed_detachment) }
% 84.82/12.68    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(p, p))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), implies(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))))), true, ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p)))))), true), true), true, ifeq(is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 84.82/12.69  = { by axiom 1 (ifeq_axiom) }
% 84.82/12.69    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(p, p))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), implies(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))))), true, is_a_theorem(implies(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p)))))), true), true, ifeq(is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 84.82/12.69  = { by axiom 1 (ifeq_axiom) R->L }
% 84.82/12.70    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(p, p))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), implies(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p)))))), true), true, ifeq(is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 84.82/12.70  = { by axiom 5 (cn_1) R->L }
% 84.82/12.70    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(p, p))), implies(not(not(implies(p, p))), not(implies(p, p)))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(p, p))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), implies(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p)))))), true), true, ifeq(is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 84.82/12.70  = { by axiom 1 (ifeq_axiom) R->L }
% 84.82/12.71    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(p, p))), implies(not(not(implies(p, p))), not(implies(p, p)))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(p, p))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), implies(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p)))))), true), true, ifeq(is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 84.82/12.71  = { by axiom 5 (cn_1) R->L }
% 84.82/12.72    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(p, p))), implies(not(not(implies(p, p))), not(implies(p, p))))), implies(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(p, p))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), implies(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p)))))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(p, p))), implies(not(not(implies(p, p))), not(implies(p, p)))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))), not(implies(p, p))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), implies(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p)))))), true), true, ifeq(is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 84.82/12.72  = { by axiom 4 (condensed_detachment) }
% 84.82/12.72    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p)))))), true), true, ifeq(is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 84.82/12.72  = { by axiom 1 (ifeq_axiom) }
% 84.82/12.72    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))))), implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p)))))), true, ifeq(is_a_theorem(implies(not(not(implies(p, p))), not(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(not(not(not(not(implies(p, p))))), not(not(not(implies(p, p))))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 84.82/12.72  = { by axiom 4 (condensed_detachment) }
% 84.82/12.72    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 84.82/12.73  = { by axiom 1 (ifeq_axiom) }
% 84.82/12.73    ifeq(ifeq(ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 84.82/12.73  = { by axiom 1 (ifeq_axiom) R->L }
% 84.82/12.73    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 84.82/12.73  = { by axiom 4 (condensed_detachment) R->L }
% 84.82/12.74    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), implies(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))))), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))))), true), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 84.82/12.74  = { by axiom 1 (ifeq_axiom) R->L }
% 84.82/12.74    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), implies(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))))), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))))), true), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 84.82/12.74  = { by axiom 5 (cn_1) R->L }
% 84.82/12.75    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), implies(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))))), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))))), true), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 84.82/12.75  = { by axiom 1 (ifeq_axiom) R->L }
% 84.82/12.75    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), implies(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))))), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))))), true), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 84.82/12.75  = { by axiom 5 (cn_1) R->L }
% 85.89/12.76    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), implies(implies(implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), implies(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))))))), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), implies(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))))), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))))), true), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 85.89/12.76  = { by axiom 4 (condensed_detachment) }
% 85.89/12.76    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))))), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))))), true), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 85.89/12.76  = { by axiom 1 (ifeq_axiom) }
% 85.89/12.77    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))))), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 85.89/12.77  = { by axiom 1 (ifeq_axiom) R->L }
% 85.89/12.77    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 85.89/12.77  = { by axiom 4 (condensed_detachment) R->L }
% 85.89/12.77    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p)))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p)))), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 85.89/12.78  = { by axiom 3 (cn_2) }
% 85.89/12.78    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p)))))), true, ifeq(true, true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 85.89/12.78  = { by axiom 1 (ifeq_axiom) }
% 85.89/12.78    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p)))))), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 85.89/12.78  = { by axiom 5 (cn_1) }
% 85.89/12.79    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 85.89/12.79  = { by axiom 1 (ifeq_axiom) }
% 85.89/12.79    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 85.89/12.79  = { by axiom 1 (ifeq_axiom) R->L }
% 85.89/12.79    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 85.89/12.79  = { by axiom 5 (cn_1) R->L }
% 85.89/12.79    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p)))), implies(implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(p, p))), not(implies(p, p))), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 85.89/12.79  = { by axiom 4 (condensed_detachment) }
% 85.89/12.80    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 85.89/12.80  = { by axiom 1 (ifeq_axiom) }
% 85.89/12.80    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p)))), implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p)))))), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), implies(not(not(implies(p, p))), not(implies(p, p))))), true, is_a_theorem(implies(implies(not(implies(p, p)), not(implies(p, p))), implies(not(not(not(implies(p, p)))), not(implies(p, p))))), true), true), true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 85.89/12.80  = { by axiom 4 (condensed_detachment) }
% 85.89/12.80    ifeq(ifeq(true, true, is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true), true, is_a_theorem(not(not(implies(p, p)))), true)
% 85.89/12.80  = { by axiom 1 (ifeq_axiom) }
% 85.89/12.80    ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true)
% 85.89/12.80  = { by axiom 1 (ifeq_axiom) R->L }
% 85.89/12.80    ifeq(true, true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 85.89/12.80  = { by axiom 4 (condensed_detachment) R->L }
% 85.89/12.80    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))), implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p)))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 85.89/12.80  = { by axiom 1 (ifeq_axiom) R->L }
% 85.89/12.80    ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))), implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 85.89/12.80  = { by axiom 5 (cn_1) R->L }
% 85.89/12.81    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))), implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 85.89/12.81  = { by axiom 1 (ifeq_axiom) R->L }
% 85.89/12.81    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))), implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 85.89/12.81  = { by axiom 5 (cn_1) R->L }
% 85.89/12.81    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))), implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))))), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))), implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 85.89/12.81  = { by axiom 4 (condensed_detachment) }
% 85.89/12.81    ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 85.89/12.82  = { by axiom 1 (ifeq_axiom) }
% 85.89/12.82    ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 85.89/12.82  = { by axiom 1 (ifeq_axiom) R->L }
% 85.89/12.82    ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 85.89/12.82  = { by axiom 4 (condensed_detachment) R->L }
% 85.89/12.82    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, ifeq(is_a_theorem(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 85.89/12.83  = { by axiom 1 (ifeq_axiom) R->L }
% 85.89/12.83    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 85.89/12.83  = { by axiom 4 (condensed_detachment) R->L }
% 85.89/12.84    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(p, p)), not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))))), implies(implies(not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), not(not(implies(p, p)))), implies(not(implies(p, p)), not(not(implies(p, p))))))), true, ifeq(is_a_theorem(implies(not(implies(p, p)), not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), not(not(implies(p, p)))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true), true, is_a_theorem(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 85.89/12.84  = { by axiom 5 (cn_1) }
% 85.89/12.84    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(p, p)), not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), not(not(implies(p, p)))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true), true, is_a_theorem(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 85.89/12.85  = { by axiom 1 (ifeq_axiom) }
% 85.89/12.85    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(p, p)), not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), not(not(implies(p, p)))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 85.89/12.85  = { by axiom 1 (ifeq_axiom) R->L }
% 86.63/12.86    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(p, p)), not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), not(not(implies(p, p)))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 86.63/12.86  = { by axiom 4 (condensed_detachment) R->L }
% 86.63/12.86    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(p), p), p), implies(p, p))), true, ifeq(is_a_theorem(implies(implies(not(p), p), p)), true, is_a_theorem(implies(p, p)), true), true), true, is_a_theorem(implies(not(implies(p, p)), not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), not(not(implies(p, p)))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 86.63/12.87  = { by axiom 3 (cn_2) }
% 86.63/12.87    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(p), p), p), implies(p, p))), true, ifeq(true, true, is_a_theorem(implies(p, p)), true), true), true, is_a_theorem(implies(not(implies(p, p)), not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), not(not(implies(p, p)))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 86.63/12.87  = { by axiom 1 (ifeq_axiom) }
% 86.63/12.88    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(p), p), p), implies(p, p))), true, is_a_theorem(implies(p, p)), true), true, is_a_theorem(implies(not(implies(p, p)), not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), not(not(implies(p, p)))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 86.63/12.88  = { by axiom 1 (ifeq_axiom) R->L }
% 86.63/12.88    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(p), p), p), implies(p, p))), true), true, is_a_theorem(implies(p, p)), true), true, is_a_theorem(implies(not(implies(p, p)), not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), not(not(implies(p, p)))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 86.63/12.89  = { by axiom 5 (cn_1) R->L }
% 86.63/12.89    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(p, implies(not(p), p)), implies(implies(implies(not(p), p), p), implies(p, p)))), true, is_a_theorem(implies(implies(implies(not(p), p), p), implies(p, p))), true), true, is_a_theorem(implies(p, p)), true), true, is_a_theorem(implies(not(implies(p, p)), not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), not(not(implies(p, p)))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 86.63/12.89  = { by axiom 1 (ifeq_axiom) R->L }
% 86.63/12.90    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(p, implies(not(p), p)), implies(implies(implies(not(p), p), p), implies(p, p)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(p), p), p), implies(p, p))), true), true), true, is_a_theorem(implies(p, p)), true), true, is_a_theorem(implies(not(implies(p, p)), not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), not(not(implies(p, p)))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 86.95/12.90  = { by axiom 2 (cn_3) R->L }
% 86.95/12.90    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(p, implies(not(p), p)), implies(implies(implies(not(p), p), p), implies(p, p)))), true, ifeq(is_a_theorem(implies(p, implies(not(p), p))), true, is_a_theorem(implies(implies(implies(not(p), p), p), implies(p, p))), true), true), true, is_a_theorem(implies(p, p)), true), true, is_a_theorem(implies(not(implies(p, p)), not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), not(not(implies(p, p)))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 86.95/12.91  = { by axiom 4 (condensed_detachment) }
% 86.95/12.91    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(p, p)), true), true, is_a_theorem(implies(not(implies(p, p)), not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), not(not(implies(p, p)))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 86.95/12.91  = { by axiom 1 (ifeq_axiom) }
% 86.95/12.91    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(p, p)), true, is_a_theorem(implies(not(implies(p, p)), not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), not(not(implies(p, p)))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 86.95/12.92  = { by axiom 1 (ifeq_axiom) R->L }
% 86.95/12.92    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(p, p)), true, is_a_theorem(implies(not(implies(p, p)), not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), not(not(implies(p, p)))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 86.95/12.92  = { by axiom 2 (cn_3) R->L }
% 86.95/12.93    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(p, p), implies(not(implies(p, p)), not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))))))), true, ifeq(is_a_theorem(implies(p, p)), true, is_a_theorem(implies(not(implies(p, p)), not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), not(not(implies(p, p)))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 86.95/12.93  = { by axiom 4 (condensed_detachment) }
% 86.95/12.93    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), not(not(implies(p, p)))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 86.95/12.94  = { by axiom 1 (ifeq_axiom) }
% 86.95/12.94    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), not(not(implies(p, p)))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true, is_a_theorem(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 86.95/12.95  = { by axiom 1 (ifeq_axiom) R->L }
% 86.95/12.95    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), not(not(implies(p, p)))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true, is_a_theorem(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 86.95/12.95  = { by axiom 4 (condensed_detachment) R->L }
% 86.95/12.96    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), not(not(implies(p, p))))), implies(implies(implies(not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), not(not(implies(p, p)))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p)))))))), true, ifeq(is_a_theorem(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), not(not(implies(p, p)))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), not(not(implies(p, p)))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), not(not(implies(p, p)))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true, is_a_theorem(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 86.95/12.96  = { by axiom 2 (cn_3) }
% 86.95/12.97    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), not(not(implies(p, p))))), implies(implies(implies(not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), not(not(implies(p, p)))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), not(not(implies(p, p)))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), not(not(implies(p, p)))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true, is_a_theorem(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 86.95/12.97  = { by axiom 1 (ifeq_axiom) }
% 86.95/12.98    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), not(not(implies(p, p))))), implies(implies(implies(not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), not(not(implies(p, p)))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), not(not(implies(p, p)))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), not(not(implies(p, p)))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true, is_a_theorem(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 86.95/12.98  = { by axiom 5 (cn_1) }
% 86.95/12.98    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), not(not(implies(p, p)))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), not(not(implies(p, p)))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true, is_a_theorem(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 86.95/12.98  = { by axiom 1 (ifeq_axiom) }
% 86.95/12.98    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), not(not(implies(p, p)))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), not(not(implies(p, p)))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true, is_a_theorem(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 86.95/12.99  = { by axiom 4 (condensed_detachment) }
% 86.95/12.99    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 86.95/13.00  = { by axiom 1 (ifeq_axiom) }
% 86.95/13.00    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 87.65/13.00  = { by axiom 1 (ifeq_axiom) R->L }
% 87.65/13.01    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 87.65/13.01  = { by axiom 4 (condensed_detachment) R->L }
% 87.65/13.02    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 87.65/13.03  = { by axiom 1 (ifeq_axiom) R->L }
% 87.65/13.04    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 87.65/13.05  = { by axiom 5 (cn_1) R->L }
% 87.65/13.05    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 87.65/13.06  = { by axiom 1 (ifeq_axiom) R->L }
% 87.65/13.07    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 87.65/13.07  = { by axiom 5 (cn_1) R->L }
% 87.65/13.09    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), implies(implies(implies(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 87.65/13.09  = { by axiom 4 (condensed_detachment) }
% 88.35/13.10    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 88.35/13.11  = { by axiom 1 (ifeq_axiom) }
% 88.35/13.11    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 88.35/13.12  = { by axiom 1 (ifeq_axiom) R->L }
% 88.35/13.12    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 88.35/13.13  = { by axiom 4 (condensed_detachment) R->L }
% 88.35/13.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 88.35/13.14  = { by axiom 3 (cn_2) }
% 88.35/13.14    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 88.35/13.14  = { by axiom 1 (ifeq_axiom) }
% 88.35/13.15    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 88.35/13.15  = { by axiom 5 (cn_1) }
% 88.35/13.16    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 88.35/13.16  = { by axiom 1 (ifeq_axiom) }
% 88.35/13.17    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 88.35/13.17  = { by axiom 1 (ifeq_axiom) R->L }
% 88.35/13.18    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 88.35/13.18  = { by axiom 5 (cn_1) R->L }
% 88.35/13.18    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), implies(implies(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 88.35/13.19  = { by axiom 4 (condensed_detachment) }
% 88.35/13.19    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 88.35/13.20  = { by axiom 1 (ifeq_axiom) }
% 89.05/13.20    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 89.05/13.21  = { by axiom 1 (ifeq_axiom) R->L }
% 89.05/13.21    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 89.05/13.21  = { by axiom 4 (condensed_detachment) R->L }
% 89.05/13.22    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))))), implies(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 89.05/13.23  = { by axiom 5 (cn_1) }
% 89.05/13.23    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 89.05/13.23  = { by axiom 1 (ifeq_axiom) }
% 89.05/13.24    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 89.05/13.24  = { by axiom 5 (cn_1) }
% 89.05/13.24    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 89.05/13.25  = { by axiom 1 (ifeq_axiom) }
% 89.05/13.25    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true, is_a_theorem(implies(implies(not(implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), implies(not(implies(p, p)), not(not(implies(p, p))))), implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 89.05/13.25  = { by axiom 4 (condensed_detachment) }
% 89.05/13.25    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 89.05/13.25  = { by axiom 1 (ifeq_axiom) }
% 89.05/13.25    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 89.05/13.25  = { by axiom 1 (ifeq_axiom) R->L }
% 89.05/13.25    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 89.05/13.26  = { by axiom 3 (cn_2) R->L }
% 89.05/13.26    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p)))), implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p)))))), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(not(implies(p, p)))), not(not(implies(p, p))))), true, is_a_theorem(implies(implies(implies(not(implies(p, p)), not(not(implies(p, p)))), implies(not(not(not(implies(p, p)))), not(not(implies(p, p))))), not(not(implies(p, p))))), true), true), true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 89.05/13.26  = { by axiom 4 (condensed_detachment) }
% 89.05/13.26    ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 89.05/13.26  = { by axiom 1 (ifeq_axiom) }
% 89.05/13.26    ifeq(is_a_theorem(implies(implies(not(not(not(implies(p, p)))), not(implies(p, p))), not(not(implies(p, p))))), true, ifeq(is_a_theorem(implies(not(not(not(implies(p, p)))), not(implies(p, p)))), true, is_a_theorem(not(not(implies(p, p)))), true), true)
% 89.05/13.26  = { by axiom 4 (condensed_detachment) }
% 89.05/13.26    true
% 89.05/13.26  % SZS output end Proof
% 89.05/13.26  
% 89.05/13.26  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------