Twee---2.7.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : LCL401-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n006.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 11:49:46 AM UTC 2026

% Result   : Unsatisfiable 106.97s 13.98s
% Output   : Proof 260.88s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : LCL401-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04  % Command  : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37  % Computer : n006.cluster.edu
% 0.10/0.37  % Model    : x86_64 x86_64
% 0.10/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37  % Memory   : 8046.5625MB
% 0.10/0.37  % OS       : Linux 6.8.0-71-generic
% 0.10/0.37  % CPULimit : 300
% 0.10/0.37  % WCLimit  : 300
% 0.10/0.37  % DateTime : Sun Sep 27 15:39:55 UTC 2026
% 0.10/0.37  % CPUTime  : 
% 0.10/0.37  Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 106.97/13.98  Command-line arguments: --no-flatten-goal
% 106.97/13.98  
% 106.97/13.98  % SZS status Unsatisfiable
% 106.97/13.98  
% 226.06/28.92  % SZS output start Proof
% 226.06/28.92  Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 226.06/28.92  Axiom 2 (cn_3): is_a_theorem(implies(X, implies(not(X), Y))) = true.
% 226.06/28.92  Axiom 3 (cn_2): is_a_theorem(implies(implies(not(X), X), X)) = true.
% 226.06/28.92  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.
% 227.28/29.06  Axiom 5 (cn_1): is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true.
% 227.28/29.06  
% 227.28/29.06  Goal 1 (prove_cn_67): is_a_theorem(implies(not(implies(x, y)), not(y))) = true.
% 227.28/29.06  Proof:
% 227.28/29.06    is_a_theorem(implies(not(implies(x, y)), not(y)))
% 227.28/29.06  = { by axiom 1 (ifeq_axiom) R->L }
% 227.28/29.06    ifeq(true, true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.06  = { by axiom 4 (condensed_detachment) R->L }
% 227.28/29.07    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(is_a_theorem(implies(y, implies(x, y))), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.07  = { by axiom 1 (ifeq_axiom) R->L }
% 227.28/29.07    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(true, true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.07  = { by axiom 4 (condensed_detachment) R->L }
% 227.28/29.07    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(y, implies(not(implies(x, y)), implies(x, y))), implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y))))), true, ifeq(is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.07  = { by axiom 5 (cn_1) }
% 227.28/29.07    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.07  = { by axiom 1 (ifeq_axiom) }
% 227.28/29.07    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.07  = { by axiom 1 (ifeq_axiom) R->L }
% 227.28/29.07    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.07  = { by axiom 4 (condensed_detachment) R->L }
% 227.28/29.07    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y)))), implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.07  = { by axiom 1 (ifeq_axiom) R->L }
% 227.28/29.07    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y)))), implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.07  = { by axiom 5 (cn_1) R->L }
% 227.28/29.07    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))))), true, is_a_theorem(implies(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y)))), implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.07  = { by axiom 1 (ifeq_axiom) R->L }
% 227.28/29.07    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))))), true, is_a_theorem(implies(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y)))), implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.07  = { by axiom 5 (cn_1) R->L }
% 227.28/29.08    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(y, y)), implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y)))), implies(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y)))), implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))))), true, is_a_theorem(implies(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y)))), implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.08  = { by axiom 4 (condensed_detachment) }
% 227.28/29.08    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.08  = { by axiom 1 (ifeq_axiom) }
% 227.28/29.08    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.08  = { by axiom 1 (ifeq_axiom) R->L }
% 227.28/29.08    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.08  = { by axiom 4 (condensed_detachment) R->L }
% 227.28/29.08    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y))), implies(y, implies(implies(y, y), implies(x, y))))), true, ifeq(is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.08  = { by axiom 1 (ifeq_axiom) R->L }
% 227.28/29.08    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y))), implies(y, implies(implies(y, y), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.08  = { by axiom 4 (condensed_detachment) R->L }
% 227.28/29.09    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(x), y), implies(not(y), y)), implies(x, implies(not(y), y))), implies(y, implies(x, implies(not(y), y))))), true, ifeq(is_a_theorem(implies(implies(implies(not(x), y), implies(not(y), y)), implies(x, implies(not(y), y)))), true, is_a_theorem(implies(y, implies(x, implies(not(y), y)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y))), implies(y, implies(implies(y, y), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.09  = { by axiom 1 (ifeq_axiom) R->L }
% 227.28/29.09    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(x), y), implies(not(y), y)), implies(x, implies(not(y), y))), implies(y, implies(x, implies(not(y), y))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(x), y), implies(not(y), y)), implies(x, implies(not(y), y)))), true), true, is_a_theorem(implies(y, implies(x, implies(not(y), y)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y))), implies(y, implies(implies(y, y), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.09  = { by axiom 5 (cn_1) R->L }
% 227.28/29.09    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(x), y), implies(not(y), y)), implies(x, implies(not(y), y))), implies(y, implies(x, implies(not(y), y))))), true, ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(x), y)), implies(implies(implies(not(x), y), implies(not(y), y)), implies(x, implies(not(y), y))))), true, is_a_theorem(implies(implies(implies(not(x), y), implies(not(y), y)), implies(x, implies(not(y), y)))), true), true, is_a_theorem(implies(y, implies(x, implies(not(y), y)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y))), implies(y, implies(implies(y, y), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.09  = { by axiom 1 (ifeq_axiom) R->L }
% 227.28/29.09    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(x), y), implies(not(y), y)), implies(x, implies(not(y), y))), implies(y, implies(x, implies(not(y), y))))), true, ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(x), y)), implies(implies(implies(not(x), y), implies(not(y), y)), implies(x, implies(not(y), y))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(x), y), implies(not(y), y)), implies(x, implies(not(y), y)))), true), true), true, is_a_theorem(implies(y, implies(x, implies(not(y), y)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y))), implies(y, implies(implies(y, y), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.09  = { by axiom 2 (cn_3) R->L }
% 227.28/29.09    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(x), y), implies(not(y), y)), implies(x, implies(not(y), y))), implies(y, implies(x, implies(not(y), y))))), true, ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(x), y)), implies(implies(implies(not(x), y), implies(not(y), y)), implies(x, implies(not(y), y))))), true, ifeq(is_a_theorem(implies(x, implies(not(x), y))), true, is_a_theorem(implies(implies(implies(not(x), y), implies(not(y), y)), implies(x, implies(not(y), y)))), true), true), true, is_a_theorem(implies(y, implies(x, implies(not(y), y)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y))), implies(y, implies(implies(y, y), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.09  = { by axiom 4 (condensed_detachment) }
% 227.28/29.09    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(x), y), implies(not(y), y)), implies(x, implies(not(y), y))), implies(y, implies(x, implies(not(y), y))))), true, ifeq(true, true, is_a_theorem(implies(y, implies(x, implies(not(y), y)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y))), implies(y, implies(implies(y, y), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.09  = { by axiom 1 (ifeq_axiom) }
% 227.28/29.10    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(x), y), implies(not(y), y)), implies(x, implies(not(y), y))), implies(y, implies(x, implies(not(y), y))))), true, is_a_theorem(implies(y, implies(x, implies(not(y), y)))), true), true, is_a_theorem(implies(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y))), implies(y, implies(implies(y, y), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.10  = { by axiom 1 (ifeq_axiom) R->L }
% 227.28/29.10    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(x), y), implies(not(y), y)), implies(x, implies(not(y), y))), implies(y, implies(x, implies(not(y), y))))), true), true, is_a_theorem(implies(y, implies(x, implies(not(y), y)))), true), true, is_a_theorem(implies(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y))), implies(y, implies(implies(y, y), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.10  = { by axiom 4 (condensed_detachment) R->L }
% 227.28/29.10    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(y), not(x)), implies(implies(not(x), y), implies(not(y), y))), implies(y, implies(implies(not(x), y), implies(not(y), y))))), true, ifeq(is_a_theorem(implies(implies(not(y), not(x)), implies(implies(not(x), y), implies(not(y), y)))), true, is_a_theorem(implies(y, implies(implies(not(x), y), implies(not(y), y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), y), implies(not(y), y)), implies(x, implies(not(y), y))), implies(y, implies(x, implies(not(y), y))))), true), true, is_a_theorem(implies(y, implies(x, implies(not(y), y)))), true), true, is_a_theorem(implies(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y))), implies(y, implies(implies(y, y), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.10  = { by axiom 1 (ifeq_axiom) R->L }
% 227.28/29.10    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(y), not(x)), implies(implies(not(x), y), implies(not(y), y))), implies(y, implies(implies(not(x), y), implies(not(y), y))))), true), true, ifeq(is_a_theorem(implies(implies(not(y), not(x)), implies(implies(not(x), y), implies(not(y), y)))), true, is_a_theorem(implies(y, implies(implies(not(x), y), implies(not(y), y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), y), implies(not(y), y)), implies(x, implies(not(y), y))), implies(y, implies(x, implies(not(y), y))))), true), true, is_a_theorem(implies(y, implies(x, implies(not(y), y)))), true), true, is_a_theorem(implies(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y))), implies(y, implies(implies(y, y), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.10  = { by axiom 5 (cn_1) R->L }
% 227.28/29.10    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(y, implies(not(y), not(x))), implies(implies(implies(not(y), not(x)), implies(implies(not(x), y), implies(not(y), y))), implies(y, implies(implies(not(x), y), implies(not(y), y)))))), true, is_a_theorem(implies(implies(implies(not(y), not(x)), implies(implies(not(x), y), implies(not(y), y))), implies(y, implies(implies(not(x), y), implies(not(y), y))))), true), true, ifeq(is_a_theorem(implies(implies(not(y), not(x)), implies(implies(not(x), y), implies(not(y), y)))), true, is_a_theorem(implies(y, implies(implies(not(x), y), implies(not(y), y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), y), implies(not(y), y)), implies(x, implies(not(y), y))), implies(y, implies(x, implies(not(y), y))))), true), true, is_a_theorem(implies(y, implies(x, implies(not(y), y)))), true), true, is_a_theorem(implies(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y))), implies(y, implies(implies(y, y), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.11  = { by axiom 1 (ifeq_axiom) R->L }
% 227.28/29.11    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(y, implies(not(y), not(x))), implies(implies(implies(not(y), not(x)), implies(implies(not(x), y), implies(not(y), y))), implies(y, implies(implies(not(x), y), implies(not(y), y)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(y), not(x)), implies(implies(not(x), y), implies(not(y), y))), implies(y, implies(implies(not(x), y), implies(not(y), y))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(y), not(x)), implies(implies(not(x), y), implies(not(y), y)))), true, is_a_theorem(implies(y, implies(implies(not(x), y), implies(not(y), y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), y), implies(not(y), y)), implies(x, implies(not(y), y))), implies(y, implies(x, implies(not(y), y))))), true), true, is_a_theorem(implies(y, implies(x, implies(not(y), y)))), true), true, is_a_theorem(implies(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y))), implies(y, implies(implies(y, y), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.11  = { by axiom 2 (cn_3) R->L }
% 227.28/29.11    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(y, implies(not(y), not(x))), implies(implies(implies(not(y), not(x)), implies(implies(not(x), y), implies(not(y), y))), implies(y, implies(implies(not(x), y), implies(not(y), y)))))), true, ifeq(is_a_theorem(implies(y, implies(not(y), not(x)))), true, is_a_theorem(implies(implies(implies(not(y), not(x)), implies(implies(not(x), y), implies(not(y), y))), implies(y, implies(implies(not(x), y), implies(not(y), y))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(y), not(x)), implies(implies(not(x), y), implies(not(y), y)))), true, is_a_theorem(implies(y, implies(implies(not(x), y), implies(not(y), y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), y), implies(not(y), y)), implies(x, implies(not(y), y))), implies(y, implies(x, implies(not(y), y))))), true), true, is_a_theorem(implies(y, implies(x, implies(not(y), y)))), true), true, is_a_theorem(implies(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y))), implies(y, implies(implies(y, y), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.11  = { by axiom 4 (condensed_detachment) }
% 227.28/29.11    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(y), not(x)), implies(implies(not(x), y), implies(not(y), y)))), true, is_a_theorem(implies(y, implies(implies(not(x), y), implies(not(y), y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), y), implies(not(y), y)), implies(x, implies(not(y), y))), implies(y, implies(x, implies(not(y), y))))), true), true, is_a_theorem(implies(y, implies(x, implies(not(y), y)))), true), true, is_a_theorem(implies(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y))), implies(y, implies(implies(y, y), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.11  = { by axiom 1 (ifeq_axiom) }
% 227.28/29.11    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(y), not(x)), implies(implies(not(x), y), implies(not(y), y)))), true, is_a_theorem(implies(y, implies(implies(not(x), y), implies(not(y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(x), y), implies(not(y), y)), implies(x, implies(not(y), y))), implies(y, implies(x, implies(not(y), y))))), true), true, is_a_theorem(implies(y, implies(x, implies(not(y), y)))), true), true, is_a_theorem(implies(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y))), implies(y, implies(implies(y, y), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.11  = { by axiom 5 (cn_1) }
% 227.28/29.11    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(y, implies(implies(not(x), y), implies(not(y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(x), y), implies(not(y), y)), implies(x, implies(not(y), y))), implies(y, implies(x, implies(not(y), y))))), true), true, is_a_theorem(implies(y, implies(x, implies(not(y), y)))), true), true, is_a_theorem(implies(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y))), implies(y, implies(implies(y, y), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.12  = { by axiom 1 (ifeq_axiom) }
% 227.28/29.12    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(y, implies(implies(not(x), y), implies(not(y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(x), y), implies(not(y), y)), implies(x, implies(not(y), y))), implies(y, implies(x, implies(not(y), y))))), true), true, is_a_theorem(implies(y, implies(x, implies(not(y), y)))), true), true, is_a_theorem(implies(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y))), implies(y, implies(implies(y, y), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.12  = { by axiom 1 (ifeq_axiom) R->L }
% 227.28/29.12    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(y, implies(implies(not(x), y), implies(not(y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(x), y), implies(not(y), y)), implies(x, implies(not(y), y))), implies(y, implies(x, implies(not(y), y))))), true), true), true, is_a_theorem(implies(y, implies(x, implies(not(y), y)))), true), true, is_a_theorem(implies(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y))), implies(y, implies(implies(y, y), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.12  = { by axiom 5 (cn_1) R->L }
% 227.28/29.13    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(y, implies(implies(not(x), y), implies(not(y), y))), implies(implies(implies(implies(not(x), y), implies(not(y), y)), implies(x, implies(not(y), y))), implies(y, implies(x, implies(not(y), y)))))), true, ifeq(is_a_theorem(implies(y, implies(implies(not(x), y), implies(not(y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(x), y), implies(not(y), y)), implies(x, implies(not(y), y))), implies(y, implies(x, implies(not(y), y))))), true), true), true, is_a_theorem(implies(y, implies(x, implies(not(y), y)))), true), true, is_a_theorem(implies(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y))), implies(y, implies(implies(y, y), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.13  = { by axiom 4 (condensed_detachment) }
% 227.28/29.13    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(y, implies(x, implies(not(y), y)))), true), true, is_a_theorem(implies(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y))), implies(y, implies(implies(y, y), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.13  = { by axiom 1 (ifeq_axiom) }
% 227.28/29.13    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(y, implies(x, implies(not(y), y)))), true, is_a_theorem(implies(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y))), implies(y, implies(implies(y, y), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.14  = { by axiom 1 (ifeq_axiom) R->L }
% 227.28/29.14    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(y, implies(x, implies(not(y), y)))), true, is_a_theorem(implies(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y))), implies(y, implies(implies(y, y), implies(x, y))))), true), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.14  = { by axiom 5 (cn_1) R->L }
% 227.28/29.14    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, implies(not(y), y))), implies(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y))), implies(y, implies(implies(y, y), implies(x, y)))))), true, ifeq(is_a_theorem(implies(y, implies(x, implies(not(y), y)))), true, is_a_theorem(implies(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y))), implies(y, implies(implies(y, y), implies(x, y))))), true), true), true, ifeq(is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.14  = { by axiom 4 (condensed_detachment) }
% 227.28/29.14    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.14  = { by axiom 1 (ifeq_axiom) }
% 227.28/29.14    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.14  = { by axiom 1 (ifeq_axiom) R->L }
% 227.28/29.14    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.14  = { by axiom 4 (condensed_detachment) R->L }
% 227.28/29.14    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(implies(implies(not(y), y), y), implies(x, y)), implies(implies(y, y), implies(x, y))))), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(x, y)), implies(implies(y, y), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.14  = { by axiom 5 (cn_1) }
% 227.28/29.14    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(x, y)), implies(implies(y, y), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.14  = { by axiom 1 (ifeq_axiom) }
% 227.28/29.14    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(x, y)), implies(implies(y, y), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.14  = { by axiom 1 (ifeq_axiom) R->L }
% 227.28/29.14    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(x, y)), implies(implies(y, y), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.14  = { by axiom 5 (cn_1) R->L }
% 227.28/29.14    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(y), y), y), implies(implies(y, y), implies(implies(not(y), y), y)))), true, is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(x, y)), implies(implies(y, y), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.14  = { by axiom 1 (ifeq_axiom) R->L }
% 227.28/29.14    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(y), y), y), implies(implies(y, y), implies(implies(not(y), y), y)))), true, ifeq(true, true, is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(x, y)), implies(implies(y, y), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.15  = { by axiom 3 (cn_2) R->L }
% 227.28/29.15    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(y), y), y), implies(implies(y, y), implies(implies(not(y), y), y)))), true, ifeq(is_a_theorem(implies(implies(not(y), y), y)), true, is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(x, y)), implies(implies(y, y), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.15  = { by axiom 4 (condensed_detachment) }
% 227.28/29.15    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(x, y)), implies(implies(y, y), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.15  = { by axiom 1 (ifeq_axiom) }
% 227.28/29.15    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(x, y)), implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.15  = { by axiom 1 (ifeq_axiom) R->L }
% 227.28/29.15    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(x, y)), implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true), true), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.15  = { by axiom 4 (condensed_detachment) R->L }
% 227.28/29.15    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(x, implies(not(y), y)), implies(implies(implies(not(y), y), y), implies(x, y))), implies(implies(implies(implies(implies(not(y), y), y), implies(x, y)), implies(implies(y, y), implies(x, y))), implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))))), true, ifeq(is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(implies(not(y), y), y), implies(x, y)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(y), y), y), implies(x, y)), implies(implies(y, y), implies(x, y))), implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(x, y)), implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true), true), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.15  = { by axiom 5 (cn_1) }
% 227.28/29.15    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(implies(not(y), y), y), implies(x, y)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(y), y), y), implies(x, y)), implies(implies(y, y), implies(x, y))), implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(x, y)), implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true), true), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.15  = { by axiom 1 (ifeq_axiom) }
% 227.28/29.15    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(implies(not(y), y), y), implies(x, y)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(y), y), y), implies(x, y)), implies(implies(y, y), implies(x, y))), implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(x, y)), implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true), true), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 227.28/29.15  = { by axiom 5 (cn_1) }
% 228.08/29.15    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(y), y), y), implies(x, y)), implies(implies(y, y), implies(x, y))), implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(x, y)), implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true), true), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.15  = { by axiom 1 (ifeq_axiom) }
% 228.08/29.16    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(y), y), y), implies(x, y)), implies(implies(y, y), implies(x, y))), implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(x, y)), implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(implies(x, implies(not(y), y)), implies(implies(y, y), implies(x, y)))), true), true), true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.16  = { by axiom 4 (condensed_detachment) }
% 228.08/29.16    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.16  = { by axiom 1 (ifeq_axiom) }
% 228.08/29.16    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.16  = { by axiom 1 (ifeq_axiom) R->L }
% 228.08/29.16    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.16  = { by axiom 5 (cn_1) R->L }
% 228.08/29.16    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(y, implies(implies(y, y), implies(x, y))), implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y)))))), true, ifeq(is_a_theorem(implies(y, implies(implies(y, y), implies(x, y)))), true, is_a_theorem(implies(implies(implies(implies(y, y), implies(x, y)), implies(not(implies(x, y)), implies(x, y))), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.16  = { by axiom 4 (condensed_detachment) }
% 228.08/29.16    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.16  = { by axiom 1 (ifeq_axiom) }
% 228.08/29.16    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.16  = { by axiom 1 (ifeq_axiom) R->L }
% 228.08/29.16    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, ifeq(true, true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.16  = { by axiom 4 (condensed_detachment) R->L }
% 228.08/29.16    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(not(implies(x, y)), implies(y, y)))), true, ifeq(is_a_theorem(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y))), true, is_a_theorem(implies(not(implies(x, y)), implies(y, y))), true), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.16  = { by axiom 3 (cn_2) }
% 228.08/29.16    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(not(implies(x, y)), implies(y, y)))), true, ifeq(true, true, is_a_theorem(implies(not(implies(x, y)), implies(y, y))), true), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.16  = { by axiom 1 (ifeq_axiom) }
% 228.08/29.16    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(not(implies(x, y)), implies(y, y)))), true, is_a_theorem(implies(not(implies(x, y)), implies(y, y))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.16  = { by axiom 1 (ifeq_axiom) R->L }
% 228.08/29.16    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(not(implies(x, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(y, y))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.17  = { by axiom 4 (condensed_detachment) R->L }
% 228.08/29.17    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y))), implies(not(implies(x, y)), implies(not(implies(y, y)), implies(y, y))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(x, y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true, is_a_theorem(implies(not(implies(x, y)), implies(not(implies(y, y)), implies(y, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(not(implies(x, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(y, y))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.17  = { by axiom 1 (ifeq_axiom) R->L }
% 228.08/29.17    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(x, y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y))), implies(not(implies(x, y)), implies(not(implies(y, y)), implies(y, y))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(x, y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true, is_a_theorem(implies(not(implies(x, y)), implies(not(implies(y, y)), implies(y, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(not(implies(x, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(y, y))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.17  = { by axiom 5 (cn_1) R->L }
% 228.08/29.17    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(implies(x, y))), implies(y, y))), implies(implies(implies(not(not(implies(x, y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y))), implies(not(implies(x, y)), implies(not(implies(y, y)), implies(y, y)))))), true, is_a_theorem(implies(implies(implies(not(not(implies(x, y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y))), implies(not(implies(x, y)), implies(not(implies(y, y)), implies(y, y))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(x, y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true, is_a_theorem(implies(not(implies(x, y)), implies(not(implies(y, y)), implies(y, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(not(implies(x, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(y, y))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.17  = { by axiom 1 (ifeq_axiom) R->L }
% 228.08/29.17    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(implies(x, y))), implies(y, y))), implies(implies(implies(not(not(implies(x, y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y))), implies(not(implies(x, y)), implies(not(implies(y, y)), implies(y, y)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(x, y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y))), implies(not(implies(x, y)), implies(not(implies(y, y)), implies(y, y))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(x, y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true, is_a_theorem(implies(not(implies(x, y)), implies(not(implies(y, y)), implies(y, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(not(implies(x, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(y, y))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.17  = { by axiom 2 (cn_3) R->L }
% 228.08/29.17    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(implies(x, y))), implies(y, y))), implies(implies(implies(not(not(implies(x, y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y))), implies(not(implies(x, y)), implies(not(implies(y, y)), implies(y, y)))))), true, ifeq(is_a_theorem(implies(not(implies(x, y)), implies(not(not(implies(x, y))), implies(y, y)))), true, is_a_theorem(implies(implies(implies(not(not(implies(x, y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y))), implies(not(implies(x, y)), implies(not(implies(y, y)), implies(y, y))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(x, y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true, is_a_theorem(implies(not(implies(x, y)), implies(not(implies(y, y)), implies(y, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(not(implies(x, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(y, y))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.17  = { by axiom 4 (condensed_detachment) }
% 228.08/29.17    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(x, y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true, is_a_theorem(implies(not(implies(x, y)), implies(not(implies(y, y)), implies(y, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(not(implies(x, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(y, y))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.18  = { by axiom 1 (ifeq_axiom) }
% 228.08/29.18    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(x, y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true, is_a_theorem(implies(not(implies(x, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(not(implies(x, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(y, y))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.18  = { by axiom 1 (ifeq_axiom) R->L }
% 228.08/29.18    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(x, y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(not(implies(x, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(y, y))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.18  = { by axiom 4 (condensed_detachment) R->L }
% 228.08/29.18    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(y, y), implies(not(implies(y, y)), not(not(implies(x, y)))))), true, ifeq(is_a_theorem(implies(y, y)), true, is_a_theorem(implies(not(implies(y, y)), not(not(implies(x, y))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(x, y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(not(implies(x, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(y, y))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.18  = { by axiom 2 (cn_3) }
% 228.08/29.18    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(y, y)), true, is_a_theorem(implies(not(implies(y, y)), not(not(implies(x, y))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(x, y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(not(implies(x, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(y, y))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.18  = { by axiom 1 (ifeq_axiom) }
% 228.08/29.18    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(y, y)), true, is_a_theorem(implies(not(implies(y, y)), not(not(implies(x, y))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(not(implies(x, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(y, y))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.18  = { by axiom 1 (ifeq_axiom) R->L }
% 228.08/29.18    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(y, y)), true), true, is_a_theorem(implies(not(implies(y, y)), not(not(implies(x, y))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(not(implies(x, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(y, y))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.18  = { by axiom 4 (condensed_detachment) R->L }
% 228.08/29.18    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(y, implies(not(y), y)), implies(implies(implies(not(y), y), y), implies(y, y)))), true, ifeq(is_a_theorem(implies(y, implies(not(y), y))), true, is_a_theorem(implies(implies(implies(not(y), y), y), implies(y, y))), true), true), true, is_a_theorem(implies(y, y)), true), true, is_a_theorem(implies(not(implies(y, y)), not(not(implies(x, y))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(not(implies(x, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(y, y))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.18  = { by axiom 2 (cn_3) }
% 228.08/29.18    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(y, implies(not(y), y)), implies(implies(implies(not(y), y), y), implies(y, y)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(y), y), y), implies(y, y))), true), true), true, is_a_theorem(implies(y, y)), true), true, is_a_theorem(implies(not(implies(y, y)), not(not(implies(x, y))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(not(implies(x, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(y, y))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.19  = { by axiom 1 (ifeq_axiom) }
% 228.08/29.19    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(y, implies(not(y), y)), implies(implies(implies(not(y), y), y), implies(y, y)))), true, is_a_theorem(implies(implies(implies(not(y), y), y), implies(y, y))), true), true, is_a_theorem(implies(y, y)), true), true, is_a_theorem(implies(not(implies(y, y)), not(not(implies(x, y))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(not(implies(x, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(y, y))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.19  = { by axiom 5 (cn_1) }
% 228.08/29.19    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(y), y), y), implies(y, y))), true), true, is_a_theorem(implies(y, y)), true), true, is_a_theorem(implies(not(implies(y, y)), not(not(implies(x, y))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(not(implies(x, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(y, y))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.19  = { by axiom 1 (ifeq_axiom) }
% 228.08/29.19    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(y), y), y), implies(y, y))), true, is_a_theorem(implies(y, y)), true), true, is_a_theorem(implies(not(implies(y, y)), not(not(implies(x, y))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(not(implies(x, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(y, y))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.19  = { by axiom 1 (ifeq_axiom) R->L }
% 228.08/29.19    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(y), y), y), implies(y, y))), true, ifeq(true, true, is_a_theorem(implies(y, y)), true), true), true, is_a_theorem(implies(not(implies(y, y)), not(not(implies(x, y))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(not(implies(x, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(y, y))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.19  = { by axiom 3 (cn_2) R->L }
% 228.08/29.19    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(y), y), y), implies(y, y))), true, ifeq(is_a_theorem(implies(implies(not(y), y), y)), true, is_a_theorem(implies(y, y)), true), true), true, is_a_theorem(implies(not(implies(y, y)), not(not(implies(x, y))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(not(implies(x, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(y, y))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.19  = { by axiom 4 (condensed_detachment) }
% 228.08/29.19    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(y, y)), not(not(implies(x, y))))), true), true, is_a_theorem(implies(implies(not(not(implies(x, y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(not(implies(x, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(y, y))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.19  = { by axiom 1 (ifeq_axiom) }
% 228.08/29.19    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(y, y)), not(not(implies(x, y))))), true, is_a_theorem(implies(implies(not(not(implies(x, y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(not(implies(x, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(y, y))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.20  = { by axiom 1 (ifeq_axiom) R->L }
% 228.08/29.20    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(y, y)), not(not(implies(x, y))))), true, is_a_theorem(implies(implies(not(not(implies(x, y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true), true), true, is_a_theorem(implies(not(implies(x, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(not(implies(x, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(y, y))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.20  = { by axiom 5 (cn_1) R->L }
% 228.08/29.20    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(y, y)), not(not(implies(x, y)))), implies(implies(not(not(implies(x, y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y))))), true, ifeq(is_a_theorem(implies(not(implies(y, y)), not(not(implies(x, y))))), true, is_a_theorem(implies(implies(not(not(implies(x, y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true), true), true, is_a_theorem(implies(not(implies(x, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(not(implies(x, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(y, y))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.20  = { by axiom 4 (condensed_detachment) }
% 228.08/29.20    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(x, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(not(implies(x, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(y, y))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.20  = { by axiom 1 (ifeq_axiom) }
% 228.08/29.20    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(x, y)), implies(not(implies(y, y)), implies(y, y)))), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(not(implies(x, y)), implies(y, y)))), true), true, is_a_theorem(implies(not(implies(x, y)), implies(y, y))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.08/29.20  = { by axiom 1 (ifeq_axiom) R->L }
% 228.40/29.20    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(x, y)), implies(not(implies(y, y)), implies(y, y)))), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(not(implies(x, y)), implies(y, y)))), true), true), true, is_a_theorem(implies(not(implies(x, y)), implies(y, y))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.40/29.20  = { by axiom 5 (cn_1) R->L }
% 228.40/29.20    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(implies(y, y)), implies(y, y))), implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(not(implies(x, y)), implies(y, y))))), true, ifeq(is_a_theorem(implies(not(implies(x, y)), implies(not(implies(y, y)), implies(y, y)))), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(not(implies(x, y)), implies(y, y)))), true), true), true, is_a_theorem(implies(not(implies(x, y)), implies(y, y))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.40/29.20  = { by axiom 4 (condensed_detachment) }
% 228.40/29.20    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(x, y)), implies(y, y))), true), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.40/29.20  = { by axiom 1 (ifeq_axiom) }
% 228.40/29.20    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(y, y)), implies(y, implies(not(implies(x, y)), implies(x, y))))), true, ifeq(is_a_theorem(implies(not(implies(x, y)), implies(y, y))), true, is_a_theorem(implies(y, implies(not(implies(x, y)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.40/29.20  = { by axiom 4 (condensed_detachment) }
% 228.40/29.20    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.40/29.20  = { by axiom 1 (ifeq_axiom) }
% 228.40/29.20    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true, is_a_theorem(implies(y, implies(x, y))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.40/29.20  = { by axiom 1 (ifeq_axiom) R->L }
% 228.40/29.20    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true, ifeq(true, true, is_a_theorem(implies(y, implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.40/29.20  = { by axiom 3 (cn_2) R->L }
% 228.40/29.20    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y)), implies(y, implies(x, y)))), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(x, y)), implies(x, y))), true, is_a_theorem(implies(y, implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.40/29.20  = { by axiom 4 (condensed_detachment) }
% 228.40/29.20    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, ifeq(true, true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.40/29.20  = { by axiom 1 (ifeq_axiom) }
% 228.40/29.20    ifeq(ifeq(is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.40/29.20  = { by axiom 1 (ifeq_axiom) R->L }
% 228.40/29.20    ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.40/29.21  = { by axiom 4 (condensed_detachment) R->L }
% 228.40/29.21    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.40/29.21  = { by axiom 1 (ifeq_axiom) R->L }
% 228.40/29.21    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.40/29.21  = { by axiom 4 (condensed_detachment) R->L }
% 228.40/29.21    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.40/29.21  = { by axiom 1 (ifeq_axiom) R->L }
% 228.40/29.21    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.40/29.22  = { by axiom 5 (cn_1) R->L }
% 228.40/29.22    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.40/29.22  = { by axiom 1 (ifeq_axiom) R->L }
% 228.40/29.22    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.40/29.22  = { by axiom 2 (cn_3) R->L }
% 228.40/29.22    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y))), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.40/29.22  = { by axiom 4 (condensed_detachment) }
% 228.40/29.22    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.40/29.23  = { by axiom 1 (ifeq_axiom) }
% 228.40/29.23    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.40/29.23  = { by axiom 1 (ifeq_axiom) R->L }
% 228.40/29.23    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.40/29.23  = { by axiom 4 (condensed_detachment) R->L }
% 228.40/29.24    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.40/29.24  = { by axiom 1 (ifeq_axiom) R->L }
% 228.40/29.24    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.40/29.25  = { by axiom 5 (cn_1) R->L }
% 228.40/29.25    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.40/29.25  = { by axiom 1 (ifeq_axiom) R->L }
% 228.40/29.25    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.40/29.26  = { by axiom 5 (cn_1) R->L }
% 228.40/29.26    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.40/29.26  = { by axiom 4 (condensed_detachment) }
% 228.40/29.26    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.40/29.27  = { by axiom 1 (ifeq_axiom) }
% 228.40/29.27    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.40/29.28  = { by axiom 1 (ifeq_axiom) R->L }
% 228.40/29.28    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.40/29.28  = { by axiom 4 (condensed_detachment) R->L }
% 228.40/29.28    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.40/29.29  = { by axiom 2 (cn_3) }
% 228.40/29.29    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 228.40/29.30  = { by axiom 1 (ifeq_axiom) }
% 228.40/29.30    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 229.21/29.30  = { by axiom 1 (ifeq_axiom) R->L }
% 229.21/29.31    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 229.21/29.31  = { by axiom 4 (condensed_detachment) R->L }
% 229.21/29.31    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true, ifeq(is_a_theorem(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 229.21/29.32  = { by axiom 5 (cn_1) }
% 229.21/29.32    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 229.21/29.33  = { by axiom 1 (ifeq_axiom) }
% 229.21/29.33    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 229.21/29.33  = { by axiom 1 (ifeq_axiom) R->L }
% 229.21/29.34    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 229.21/29.34  = { by axiom 4 (condensed_detachment) R->L }
% 229.21/29.35    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(not(y), y), y)), not(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), implies(implies(not(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y))))), true, ifeq(is_a_theorem(implies(not(implies(implies(not(y), y), y)), not(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true, is_a_theorem(implies(implies(not(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true), true, is_a_theorem(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 229.21/29.35  = { by axiom 5 (cn_1) }
% 229.21/29.36    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(implies(not(y), y), y)), not(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true, is_a_theorem(implies(implies(not(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true), true, is_a_theorem(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 229.21/29.36  = { by axiom 1 (ifeq_axiom) }
% 229.21/29.36    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(implies(not(y), y), y)), not(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true, is_a_theorem(implies(implies(not(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, is_a_theorem(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 229.21/29.37  = { by axiom 1 (ifeq_axiom) R->L }
% 229.21/29.37    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(implies(not(y), y), y)), not(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true, is_a_theorem(implies(implies(not(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, is_a_theorem(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 229.21/29.38  = { by axiom 3 (cn_2) R->L }
% 229.21/29.38    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(y), y), y)), true, is_a_theorem(implies(not(implies(implies(not(y), y), y)), not(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true, is_a_theorem(implies(implies(not(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, is_a_theorem(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 229.21/29.39  = { by axiom 1 (ifeq_axiom) R->L }
% 229.21/29.39    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(y), y), y)), true, is_a_theorem(implies(not(implies(implies(not(y), y), y)), not(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, is_a_theorem(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 229.21/29.39  = { by axiom 2 (cn_3) R->L }
% 229.21/29.40    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(y), y), y), implies(not(implies(implies(not(y), y), y)), not(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))))), true, ifeq(is_a_theorem(implies(implies(not(y), y), y)), true, is_a_theorem(implies(not(implies(implies(not(y), y), y)), not(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, is_a_theorem(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 230.02/29.40  = { by axiom 4 (condensed_detachment) }
% 230.02/29.41    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, is_a_theorem(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 230.02/29.41  = { by axiom 1 (ifeq_axiom) }
% 230.02/29.42    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true, is_a_theorem(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 230.02/29.42  = { by axiom 1 (ifeq_axiom) R->L }
% 230.02/29.43    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true, is_a_theorem(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 230.02/29.43  = { by axiom 4 (condensed_detachment) R->L }
% 230.02/29.44    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(y), y), y))), implies(implies(implies(not(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))))), true, ifeq(is_a_theorem(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(y), y), y)))), true, is_a_theorem(implies(implies(implies(not(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true, is_a_theorem(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 230.02/29.45  = { by axiom 2 (cn_3) }
% 230.02/29.45    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(y), y), y))), implies(implies(implies(not(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true, is_a_theorem(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 230.02/29.45  = { by axiom 1 (ifeq_axiom) }
% 230.02/29.46    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(y), y), y))), implies(implies(implies(not(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))))), true, is_a_theorem(implies(implies(implies(not(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true, is_a_theorem(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 230.02/29.46  = { by axiom 5 (cn_1) }
% 230.02/29.47    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(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true, is_a_theorem(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 230.02/29.47  = { by axiom 1 (ifeq_axiom) }
% 230.02/29.47    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(y), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true, is_a_theorem(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 230.02/29.48  = { by axiom 4 (condensed_detachment) }
% 230.02/29.49    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 230.02/29.50  = { by axiom 1 (ifeq_axiom) }
% 230.82/29.50    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 230.82/29.52  = { by axiom 1 (ifeq_axiom) R->L }
% 230.82/29.52    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 230.82/29.55  = { by axiom 4 (condensed_detachment) R->L }
% 230.82/29.56    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), 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% 230.82/29.58  = { by axiom 1 (ifeq_axiom) R->L }
% 230.82/29.59    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), 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y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 231.61/29.61  = { by axiom 5 (cn_1) R->L }
% 231.61/29.63    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 231.61/29.64  = { by axiom 1 (ifeq_axiom) R->L }
% 231.61/29.65    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), 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implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, 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% 231.61/29.66  = { by axiom 5 (cn_1) R->L }
% 231.61/29.67    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, 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% 231.61/29.68  = { by axiom 4 (condensed_detachment) }
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not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 232.44/29.71  = { by axiom 1 (ifeq_axiom) }
% 232.44/29.71    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 232.44/29.73  = { by axiom 1 (ifeq_axiom) R->L }
% 232.44/29.73    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 232.44/29.74  = { by axiom 4 (condensed_detachment) R->L }
% 232.44/29.75    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))))), true, ifeq(is_a_theorem(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 232.44/29.77  = { by axiom 3 (cn_2) }
% 232.44/29.77    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 232.44/29.78  = { by axiom 1 (ifeq_axiom) }
% 233.21/29.80    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 233.21/29.82  = { by axiom 5 (cn_1) }
% 233.21/29.83    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 233.21/29.84  = { by axiom 1 (ifeq_axiom) }
% 233.21/29.85    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 233.21/29.86  = { by axiom 1 (ifeq_axiom) R->L }
% 233.21/29.86    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 233.21/29.87  = { by axiom 5 (cn_1) R->L }
% 233.21/29.88    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 233.21/29.88  = { by axiom 4 (condensed_detachment) }
% 233.21/29.89    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 233.21/29.89  = { by axiom 1 (ifeq_axiom) }
% 233.21/29.89    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 233.21/29.90  = { by axiom 4 (condensed_detachment) }
% 233.21/29.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 234.01/29.90  = { by axiom 1 (ifeq_axiom) }
% 234.01/29.91    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 234.01/29.91  = { by axiom 1 (ifeq_axiom) R->L }
% 234.01/29.91    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 234.01/29.91  = { by axiom 4 (condensed_detachment) R->L }
% 234.01/29.92    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 234.01/29.92  = { by axiom 5 (cn_1) }
% 234.01/29.93    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 234.01/29.93  = { by axiom 1 (ifeq_axiom) }
% 234.01/29.93    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 234.01/29.94  = { by axiom 1 (ifeq_axiom) R->L }
% 234.01/29.94    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 234.01/29.95  = { by axiom 5 (cn_1) R->L }
% 234.01/29.95    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 234.01/29.95  = { by axiom 1 (ifeq_axiom) R->L }
% 234.01/29.96    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 234.01/29.96  = { by axiom 3 (cn_2) R->L }
% 234.01/29.96    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true, ifeq(is_a_theorem(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 234.01/29.96  = { by axiom 4 (condensed_detachment) }
% 234.01/29.97    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 234.01/29.97  = { by axiom 1 (ifeq_axiom) }
% 234.01/29.97    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(y), y), y)), implies(implies(not(y), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(y), y), y), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 234.01/29.97  = { by axiom 4 (condensed_detachment) }
% 234.01/29.97    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 234.01/29.98  = { by axiom 1 (ifeq_axiom) }
% 234.01/29.98    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 234.01/29.99  = { by axiom 1 (ifeq_axiom) R->L }
% 234.01/29.99    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 234.01/30.00  = { by axiom 4 (condensed_detachment) R->L }
% 234.01/30.00    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 234.01/30.01  = { by axiom 1 (ifeq_axiom) R->L }
% 234.01/30.01    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 234.01/30.02  = { by axiom 5 (cn_1) R->L }
% 234.01/30.03    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 234.01/30.03  = { by axiom 1 (ifeq_axiom) R->L }
% 234.01/30.04    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 234.01/30.04  = { by axiom 5 (cn_1) R->L }
% 234.01/30.05    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), implies(implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 234.01/30.05  = { by axiom 4 (condensed_detachment) }
% 234.01/30.06    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 235.22/30.06  = { by axiom 1 (ifeq_axiom) }
% 235.22/30.06    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 235.22/30.07  = { by axiom 1 (ifeq_axiom) R->L }
% 235.22/30.07    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 235.22/30.08  = { by axiom 4 (condensed_detachment) R->L }
% 235.22/30.08    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true, ifeq(is_a_theorem(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 235.22/30.09  = { by axiom 3 (cn_2) }
% 235.22/30.09    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 235.22/30.09  = { by axiom 1 (ifeq_axiom) }
% 235.22/30.10    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 235.22/30.10  = { by axiom 5 (cn_1) }
% 235.22/30.11    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 235.22/30.11  = { by axiom 1 (ifeq_axiom) }
% 235.22/30.11    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 235.22/30.12  = { by axiom 1 (ifeq_axiom) R->L }
% 235.22/30.12    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 235.22/30.12  = { by axiom 5 (cn_1) R->L }
% 235.22/30.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 235.22/30.13  = { by axiom 4 (condensed_detachment) }
% 235.22/30.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 235.22/30.13  = { by axiom 1 (ifeq_axiom) }
% 235.22/30.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(not(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), y), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 235.22/30.13  = { by axiom 4 (condensed_detachment) }
% 235.22/30.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 235.22/30.13  = { by axiom 1 (ifeq_axiom) }
% 235.22/30.14    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 235.22/30.14  = { by axiom 1 (ifeq_axiom) R->L }
% 235.22/30.14    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 235.22/30.14  = { by axiom 4 (condensed_detachment) R->L }
% 235.22/30.14    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))))), true, ifeq(is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 235.22/30.14  = { by axiom 5 (cn_1) }
% 235.22/30.14    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 235.22/30.14  = { by axiom 1 (ifeq_axiom) }
% 235.22/30.14    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 235.22/30.14  = { by axiom 5 (cn_1) }
% 235.22/30.14    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 235.22/30.14  = { by axiom 1 (ifeq_axiom) }
% 235.22/30.15    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), y), implies(not(y), y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true, is_a_theorem(implies(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y))), true), true), true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 235.22/30.15  = { by axiom 4 (condensed_detachment) }
% 235.22/30.15    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 235.22/30.15  = { by axiom 1 (ifeq_axiom) }
% 235.22/30.15    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 235.22/30.15  = { by axiom 1 (ifeq_axiom) R->L }
% 235.22/30.15    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 235.22/30.15  = { by axiom 4 (condensed_detachment) R->L }
% 235.22/30.15    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 235.22/30.15  = { by axiom 1 (ifeq_axiom) R->L }
% 235.22/30.16    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 236.02/30.16  = { by axiom 4 (condensed_detachment) R->L }
% 236.02/30.16    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(x, y)), not(y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 236.02/30.16  = { by axiom 1 (ifeq_axiom) R->L }
% 236.02/30.17    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(x, y)), not(y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 236.02/30.17  = { by axiom 5 (cn_1) R->L }
% 236.02/30.17    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), implies(not(implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(x, y)), not(y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(x, y)), not(y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 236.02/30.17  = { by axiom 1 (ifeq_axiom) R->L }
% 236.02/30.17    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), implies(not(implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(x, y)), not(y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(x, y)), not(y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 236.02/30.18  = { by axiom 2 (cn_3) R->L }
% 236.02/30.18    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), implies(not(implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(x, y)), not(y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), implies(not(implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(x, y)), not(y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 236.02/30.18  = { by axiom 4 (condensed_detachment) }
% 236.02/30.18    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 236.02/30.18  = { by axiom 1 (ifeq_axiom) }
% 236.02/30.19    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 236.02/30.19  = { by axiom 1 (ifeq_axiom) R->L }
% 236.02/30.19    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 236.02/30.19  = { by axiom 5 (cn_1) R->L }
% 236.02/30.19    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), implies(implies(not(implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 236.02/30.20  = { by axiom 1 (ifeq_axiom) R->L }
% 236.02/30.20    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), implies(implies(not(implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 236.02/30.20  = { by axiom 3 (cn_2) R->L }
% 236.38/30.21    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), implies(implies(not(implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 236.38/30.21  = { by axiom 4 (condensed_detachment) }
% 236.38/30.21    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 236.38/30.21  = { by axiom 1 (ifeq_axiom) }
% 236.38/30.21    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 236.38/30.22  = { by axiom 1 (ifeq_axiom) R->L }
% 236.38/30.22    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 236.38/30.22  = { by axiom 5 (cn_1) R->L }
% 236.38/30.22    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 236.38/30.22  = { by axiom 4 (condensed_detachment) }
% 236.38/30.23    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 236.38/30.23  = { by axiom 1 (ifeq_axiom) }
% 236.38/30.23    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 236.38/30.24  = { by axiom 1 (ifeq_axiom) R->L }
% 236.38/30.24    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 236.38/30.25  = { by axiom 4 (condensed_detachment) R->L }
% 236.38/30.25    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 236.38/30.26  = { by axiom 1 (ifeq_axiom) R->L }
% 236.38/30.26    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 236.38/30.27  = { by axiom 4 (condensed_detachment) R->L }
% 236.38/30.28    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 236.38/30.29  = { by axiom 5 (cn_1) }
% 236.38/30.29    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 237.16/30.30  = { by axiom 1 (ifeq_axiom) }
% 237.16/30.31    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 237.16/30.32  = { by axiom 1 (ifeq_axiom) R->L }
% 237.16/30.33    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 237.16/30.34  = { by axiom 5 (cn_1) R->L }
% 237.16/30.34    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 237.16/30.35  = { by axiom 1 (ifeq_axiom) R->L }
% 237.16/30.36    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 237.16/30.36  = { by axiom 3 (cn_2) R->L }
% 237.16/30.37    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 237.16/30.39  = { by axiom 4 (condensed_detachment) }
% 237.16/30.39    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 237.98/30.41  = { by axiom 1 (ifeq_axiom) }
% 237.98/30.42    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 237.98/30.43  = { by axiom 1 (ifeq_axiom) R->L }
% 237.98/30.44    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 237.98/30.45  = { by axiom 4 (condensed_detachment) R->L }
% 237.98/30.46    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 237.98/30.47  = { by axiom 5 (cn_1) }
% 237.98/30.49    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 237.98/30.49  = { by axiom 1 (ifeq_axiom) }
% 238.76/30.50    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 238.76/30.51  = { by axiom 5 (cn_1) }
% 238.76/30.52    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 238.76/30.52  = { by axiom 1 (ifeq_axiom) }
% 238.76/30.53    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 238.76/30.53  = { by axiom 4 (condensed_detachment) }
% 238.76/30.54    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 238.76/30.54  = { by axiom 1 (ifeq_axiom) }
% 238.76/30.54    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 238.76/30.55  = { by axiom 1 (ifeq_axiom) R->L }
% 238.76/30.55    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 238.76/30.55  = { by axiom 4 (condensed_detachment) R->L }
% 238.76/30.56    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true, ifeq(is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 238.76/30.56  = { by axiom 5 (cn_1) }
% 238.76/30.57    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 238.76/30.57  = { by axiom 1 (ifeq_axiom) }
% 238.76/30.58    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 238.76/30.60  = { by axiom 1 (ifeq_axiom) R->L }
% 239.45/30.61    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 239.45/30.62  = { by axiom 4 (condensed_detachment) R->L }
% 239.45/30.62    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 239.45/30.63  = { by axiom 1 (ifeq_axiom) R->L }
% 239.45/30.64    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 239.45/30.65  = { by axiom 5 (cn_1) R->L }
% 239.45/30.66    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 239.45/30.67  = { by axiom 1 (ifeq_axiom) R->L }
% 239.45/30.68    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(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 239.45/30.68  = { by axiom 5 (cn_1) R->L }
% 239.45/30.69    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 239.45/30.70  = { by axiom 4 (condensed_detachment) }
% 239.45/30.70    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 240.26/30.72  = { by axiom 1 (ifeq_axiom) }
% 240.26/30.72    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 240.26/30.73  = { by axiom 1 (ifeq_axiom) R->L }
% 240.26/30.74    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 240.26/30.75  = { by axiom 4 (condensed_detachment) R->L }
% 240.26/30.76    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(implies(x, y)), not(y)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y))))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(implies(x, y)), not(y)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 240.26/30.78  = { by axiom 1 (ifeq_axiom) R->L }
% 240.26/30.79    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(implies(x, y)), not(y)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(implies(x, y)), not(y)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 240.26/30.80  = { by axiom 5 (cn_1) R->L }
% 240.94/30.81    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(implies(x, y)), not(y)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(implies(x, y)), not(y)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(implies(x, y)), not(y)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 240.94/30.82  = { by axiom 1 (ifeq_axiom) R->L }
% 240.94/30.83    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(implies(x, y)), not(y)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(implies(x, y)), not(y)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(implies(x, y)), not(y)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 240.94/30.83  = { by axiom 2 (cn_3) R->L }
% 240.94/30.84    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(implies(x, y)), not(y)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))))))), true, ifeq(is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(implies(x, y)), not(y)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(implies(x, y)), not(y)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 240.94/30.85  = { by axiom 4 (condensed_detachment) }
% 240.94/30.86    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(implies(x, y)), not(y)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 240.94/30.87  = { by axiom 1 (ifeq_axiom) }
% 240.94/30.88    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(implies(x, y)), not(y)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 240.94/30.89  = { by axiom 1 (ifeq_axiom) R->L }
% 240.94/30.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(implies(x, y)), not(y)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 241.71/30.91  = { by axiom 5 (cn_1) R->L }
% 241.71/30.91    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(implies(x, y)), not(y)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(implies(x, y)), not(y)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 241.71/30.92  = { by axiom 1 (ifeq_axiom) R->L }
% 241.71/30.93    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(implies(x, y)), not(y)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y))))))), true, ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(implies(x, y)), not(y)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 241.71/30.94  = { by axiom 3 (cn_2) R->L }
% 241.71/30.94    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(implies(x, y)), not(y)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y))))))), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(implies(x, y)), not(y)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 241.71/30.95  = { by axiom 4 (condensed_detachment) }
% 241.71/30.96    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 241.71/30.96  = { by axiom 1 (ifeq_axiom) }
% 241.71/30.97    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 241.71/30.97  = { by axiom 1 (ifeq_axiom) R->L }
% 241.71/30.98    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 241.71/30.99  = { by axiom 5 (cn_1) R->L }
% 241.71/30.99    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y))))), implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, ifeq(is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 241.71/31.00  = { by axiom 4 (condensed_detachment) }
% 241.71/31.00    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 241.71/31.01  = { by axiom 1 (ifeq_axiom) }
% 241.71/31.01    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 241.71/31.02  = { by axiom 1 (ifeq_axiom) R->L }
% 241.71/31.03    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 241.71/31.03  = { by axiom 4 (condensed_detachment) R->L }
% 241.71/31.04    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true, ifeq(is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 241.71/31.05  = { by axiom 5 (cn_1) }
% 241.71/31.06    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 241.71/31.07  = { by axiom 1 (ifeq_axiom) }
% 241.71/31.08    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 241.71/31.09  = { by axiom 1 (ifeq_axiom) R->L }
% 241.71/31.10    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 241.71/31.11  = { by axiom 4 (condensed_detachment) R->L }
% 243.47/31.12    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))))), true, ifeq(is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 243.47/31.13  = { by axiom 5 (cn_1) }
% 243.47/31.14    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 243.47/31.15  = { by axiom 1 (ifeq_axiom) }
% 243.47/31.16    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 243.47/31.18  = { by axiom 1 (ifeq_axiom) R->L }
% 243.47/31.19    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 243.47/31.22  = { by axiom 5 (cn_1) R->L }
% 244.39/31.23    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 244.39/31.26  = { by axiom 1 (ifeq_axiom) R->L }
% 244.39/31.27    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 244.39/31.29  = { by axiom 4 (condensed_detachment) R->L }
% 245.04/31.31    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))))), true, ifeq(is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 245.04/31.33  = { by axiom 2 (cn_3) }
% 245.04/31.34    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 245.04/31.36  = { by axiom 1 (ifeq_axiom) }
% 245.04/31.37    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 245.04/31.38  = { by axiom 5 (cn_1) }
% 245.04/31.40    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 245.87/31.41  = { by axiom 1 (ifeq_axiom) }
% 245.87/31.42    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))))), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 245.87/31.44  = { by axiom 4 (condensed_detachment) }
% 245.87/31.45    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 245.87/31.47  = { by axiom 1 (ifeq_axiom) }
% 245.87/31.48    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 245.87/31.50  = { by axiom 1 (ifeq_axiom) R->L }
% 246.61/31.51    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))))), true, ifeq(true, true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 246.61/31.54  = { by axiom 4 (condensed_detachment) R->L }
% 246.61/31.55    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))))), true, ifeq(is_a_theorem(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 246.61/31.57  = { by axiom 2 (cn_3) }
% 246.61/31.58    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 246.61/31.59  = { by axiom 1 (ifeq_axiom) }
% 246.61/31.60    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 246.61/31.60  = { by axiom 5 (cn_1) }
% 247.44/31.61    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 247.44/31.62  = { by axiom 1 (ifeq_axiom) }
% 247.44/31.63    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(implies(not(implies(x, y)), not(y))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 247.44/31.63  = { by axiom 4 (condensed_detachment) }
% 247.44/31.64    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 247.44/31.64  = { by axiom 1 (ifeq_axiom) }
% 247.44/31.64    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 247.44/31.65  = { by axiom 4 (condensed_detachment) }
% 247.44/31.65    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 247.44/31.66  = { by axiom 1 (ifeq_axiom) }
% 247.44/31.66    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 247.44/31.67  = { by axiom 1 (ifeq_axiom) R->L }
% 247.44/31.67    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 247.44/31.68  = { by axiom 4 (condensed_detachment) R->L }
% 247.44/31.68    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 247.44/31.69  = { by axiom 5 (cn_1) }
% 247.44/31.70    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 248.22/31.71  = { by axiom 1 (ifeq_axiom) }
% 248.22/31.71    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 248.22/31.72  = { by axiom 1 (ifeq_axiom) R->L }
% 248.22/31.72    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 248.22/31.73  = { by axiom 5 (cn_1) R->L }
% 248.22/31.74    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 248.22/31.74  = { by axiom 1 (ifeq_axiom) R->L }
% 248.22/31.75    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 248.22/31.75  = { by axiom 3 (cn_2) R->L }
% 248.22/31.76    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 248.22/31.76  = { by axiom 4 (condensed_detachment) }
% 248.22/31.77    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 248.22/31.77  = { by axiom 1 (ifeq_axiom) }
% 248.22/31.77    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 248.22/31.78  = { by axiom 4 (condensed_detachment) }
% 248.22/31.78    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 248.22/31.78  = { by axiom 1 (ifeq_axiom) }
% 248.22/31.79    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 248.22/31.79  = { by axiom 1 (ifeq_axiom) R->L }
% 248.22/31.79    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 248.22/31.79  = { by axiom 4 (condensed_detachment) R->L }
% 248.22/31.80    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 248.22/31.80  = { by axiom 3 (cn_2) }
% 248.22/31.80    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, ifeq(true, true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 249.04/31.81  = { by axiom 1 (ifeq_axiom) }
% 249.04/31.81    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 249.04/31.82  = { by axiom 1 (ifeq_axiom) R->L }
% 249.04/31.82    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 249.04/31.83  = { by axiom 5 (cn_1) R->L }
% 249.04/31.83    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 249.04/31.84  = { by axiom 1 (ifeq_axiom) R->L }
% 249.04/31.84    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 249.04/31.84  = { by axiom 2 (cn_3) R->L }
% 249.04/31.84    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true, ifeq(is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 249.04/31.85  = { by axiom 4 (condensed_detachment) }
% 249.04/31.85    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 249.04/31.85  = { by axiom 1 (ifeq_axiom) }
% 249.04/31.85    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, ifeq(is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 249.04/31.85  = { by axiom 4 (condensed_detachment) }
% 249.04/31.85    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 249.04/31.86  = { by axiom 1 (ifeq_axiom) }
% 249.04/31.86    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 249.04/31.86  = { by axiom 1 (ifeq_axiom) R->L }
% 249.04/31.86    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 249.04/31.86  = { by axiom 4 (condensed_detachment) R->L }
% 249.04/31.87    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 249.04/31.87  = { by axiom 1 (ifeq_axiom) R->L }
% 249.04/31.87    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 249.04/31.88  = { by axiom 4 (condensed_detachment) R->L }
% 249.04/31.88    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 249.04/31.88  = { by axiom 3 (cn_2) }
% 249.04/31.88    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 249.04/31.89  = { by axiom 1 (ifeq_axiom) }
% 249.04/31.89    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 249.04/31.89  = { by axiom 5 (cn_1) }
% 249.04/31.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 249.04/31.90  = { by axiom 1 (ifeq_axiom) }
% 249.04/31.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 249.82/31.90  = { by axiom 1 (ifeq_axiom) R->L }
% 249.82/31.91    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 249.82/31.91  = { by axiom 5 (cn_1) R->L }
% 249.82/31.91    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 249.82/31.91  = { by axiom 4 (condensed_detachment) }
% 249.82/31.92    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 249.82/31.92  = { by axiom 1 (ifeq_axiom) }
% 249.82/31.92    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 249.82/31.92  = { by axiom 1 (ifeq_axiom) R->L }
% 249.82/31.92    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 249.82/31.93  = { by axiom 4 (condensed_detachment) R->L }
% 249.82/31.93    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y)))), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 249.82/31.93  = { by axiom 1 (ifeq_axiom) R->L }
% 249.82/31.93    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 249.82/31.93  = { by axiom 4 (condensed_detachment) R->L }
% 249.82/31.94    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y)))), implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y)))))), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))))), true), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 249.82/31.94  = { by axiom 5 (cn_1) }
% 249.82/31.94    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))))), true), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 249.82/31.95  = { by axiom 1 (ifeq_axiom) }
% 249.82/31.95    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 249.82/31.95  = { by axiom 1 (ifeq_axiom) R->L }
% 249.82/31.95    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 249.82/31.96  = { by axiom 4 (condensed_detachment) R->L }
% 249.82/31.96    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(y), not(y))), not(not(implies(not(implies(x, y)), not(y))))), implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y)))))), true, ifeq(is_a_theorem(implies(not(implies(not(y), not(y))), not(not(implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 249.82/31.96  = { by axiom 5 (cn_1) }
% 249.82/31.97    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(not(y), not(y))), not(not(implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 249.82/31.97  = { by axiom 1 (ifeq_axiom) }
% 249.82/31.97    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(not(y), not(y))), not(not(implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 249.82/31.98  = { by axiom 1 (ifeq_axiom) R->L }
% 249.82/31.98    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(not(y), not(y))), not(not(implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 249.82/31.98  = { by axiom 4 (condensed_detachment) R->L }
% 249.82/31.98    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(y), not(y)))), true, ifeq(is_a_theorem(implies(implies(not(not(y)), not(y)), not(y))), true, is_a_theorem(implies(not(y), not(y))), true), true), true, is_a_theorem(implies(not(implies(not(y), not(y))), not(not(implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 249.82/31.99  = { by axiom 3 (cn_2) }
% 249.82/31.99    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(y), not(y)))), true, ifeq(true, true, is_a_theorem(implies(not(y), not(y))), true), true), true, is_a_theorem(implies(not(implies(not(y), not(y))), not(not(implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 249.82/32.00  = { by axiom 1 (ifeq_axiom) }
% 249.82/32.00    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(y), not(y)))), true, is_a_theorem(implies(not(y), not(y))), true), true, is_a_theorem(implies(not(implies(not(y), not(y))), not(not(implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 249.82/32.00  = { by axiom 1 (ifeq_axiom) R->L }
% 249.82/32.00    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), not(y))), true), true, is_a_theorem(implies(not(implies(not(y), not(y))), not(not(implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 250.63/32.01  = { by axiom 5 (cn_1) R->L }
% 250.63/32.01    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(y), implies(not(not(y)), not(y))), implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(y), not(y))))), true, is_a_theorem(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), not(y))), true), true, is_a_theorem(implies(not(implies(not(y), not(y))), not(not(implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 250.63/32.02  = { by axiom 1 (ifeq_axiom) R->L }
% 250.63/32.02    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(y), implies(not(not(y)), not(y))), implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(y), not(y))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(y), not(y)))), true), true), true, is_a_theorem(implies(not(y), not(y))), true), true, is_a_theorem(implies(not(implies(not(y), not(y))), not(not(implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 250.63/32.02  = { by axiom 2 (cn_3) R->L }
% 250.63/32.02    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(y), implies(not(not(y)), not(y))), implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(y), not(y))))), true, ifeq(is_a_theorem(implies(not(y), implies(not(not(y)), not(y)))), true, is_a_theorem(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(y), not(y)))), true), true), true, is_a_theorem(implies(not(y), not(y))), true), true, is_a_theorem(implies(not(implies(not(y), not(y))), not(not(implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 250.63/32.03  = { by axiom 4 (condensed_detachment) }
% 250.63/32.03    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(y), not(y))), true), true, is_a_theorem(implies(not(implies(not(y), not(y))), not(not(implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 250.63/32.03  = { by axiom 1 (ifeq_axiom) }
% 250.63/32.04    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(y), not(y))), true, is_a_theorem(implies(not(implies(not(y), not(y))), not(not(implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 250.63/32.04  = { by axiom 1 (ifeq_axiom) R->L }
% 250.63/32.04    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(y), not(y))), true, is_a_theorem(implies(not(implies(not(y), not(y))), not(not(implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 250.63/32.05  = { by axiom 2 (cn_3) R->L }
% 250.63/32.05    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(y), not(y)), implies(not(implies(not(y), not(y))), not(not(implies(not(implies(x, y)), not(y))))))), true, ifeq(is_a_theorem(implies(not(y), not(y))), true, is_a_theorem(implies(not(implies(not(y), not(y))), not(not(implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 250.63/32.05  = { by axiom 4 (condensed_detachment) }
% 250.63/32.05    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 250.63/32.06  = { by axiom 1 (ifeq_axiom) }
% 250.63/32.06    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 250.63/32.07  = { by axiom 1 (ifeq_axiom) R->L }
% 250.63/32.07    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 250.63/32.07  = { by axiom 4 (condensed_detachment) R->L }
% 250.63/32.08    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(y), not(y)))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))))), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(y), not(y))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 250.63/32.08  = { by axiom 2 (cn_3) }
% 250.63/32.08    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(y), not(y)))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 250.63/32.09  = { by axiom 1 (ifeq_axiom) }
% 250.63/32.09    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(y), not(y)))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 250.63/32.09  = { by axiom 5 (cn_1) }
% 250.63/32.10    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 250.63/32.10  = { by axiom 1 (ifeq_axiom) }
% 250.63/32.10    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y)))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), implies(not(y), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(not(y), not(y))), implies(not(y), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 250.63/32.11  = { by axiom 4 (condensed_detachment) }
% 250.63/32.11    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 250.63/32.11  = { by axiom 1 (ifeq_axiom) }
% 250.63/32.11    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))))), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y)))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 250.63/32.12  = { by axiom 1 (ifeq_axiom) R->L }
% 250.63/32.12    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))))), true, ifeq(true, true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y)))), true), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 250.63/32.12  = { by axiom 3 (cn_2) R->L }
% 250.63/32.12    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(y), not(y))), implies(not(y), not(y))), implies(not(y), not(y)))), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y)))), true), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 250.63/32.12  = { by axiom 4 (condensed_detachment) }
% 250.63/32.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, ifeq(true, true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 250.63/32.13  = { by axiom 1 (ifeq_axiom) }
% 250.63/32.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 250.63/32.13  = { by axiom 1 (ifeq_axiom) R->L }
% 250.63/32.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 250.63/32.14  = { by axiom 4 (condensed_detachment) R->L }
% 250.63/32.14    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))), implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true, ifeq(is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 250.63/32.14  = { by axiom 5 (cn_1) }
% 250.63/32.14    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 250.63/32.15  = { by axiom 1 (ifeq_axiom) }
% 250.63/32.15    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 250.63/32.15  = { by axiom 1 (ifeq_axiom) R->L }
% 250.63/32.15    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 250.63/32.16  = { by axiom 4 (condensed_detachment) R->L }
% 250.63/32.16    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(implies(x, y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))), implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(implies(x, y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 250.63/32.17  = { by axiom 1 (ifeq_axiom) R->L }
% 250.63/32.17    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(y)), not(y)), not(y)), implies(not(implies(x, y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))), implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(implies(x, y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 250.63/32.17  = { by axiom 5 (cn_1) R->L }
% 250.63/32.17    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(implies(x, y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))), implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(implies(x, y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 250.63/32.18  = { by axiom 1 (ifeq_axiom) R->L }
% 250.63/32.18    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(implies(x, y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))), implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(implies(x, y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 250.63/32.18  = { by axiom 5 (cn_1) R->L }
% 250.63/32.19    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(implies(x, y)), not(y)))), implies(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(implies(x, y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))), implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(implies(x, y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))), implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(implies(x, y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 250.63/32.19  = { by axiom 4 (condensed_detachment) }
% 250.63/32.19    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(implies(x, y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 250.63/32.20  = { by axiom 1 (ifeq_axiom) }
% 250.63/32.20    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(implies(x, y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 250.63/32.20  = { by axiom 1 (ifeq_axiom) R->L }
% 250.63/32.20    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(implies(x, y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 250.63/32.21  = { by axiom 4 (condensed_detachment) R->L }
% 250.63/32.21    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(implies(not(y), not(y)), implies(implies(not(not(y)), not(y)), not(y))))), true, ifeq(is_a_theorem(implies(implies(not(not(y)), not(y)), not(y))), true, is_a_theorem(implies(implies(not(y), not(y)), implies(implies(not(not(y)), not(y)), not(y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(implies(x, y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 250.63/32.21  = { by axiom 3 (cn_2) }
% 250.63/32.22    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(implies(not(y), not(y)), implies(implies(not(not(y)), not(y)), not(y))))), true, ifeq(true, true, is_a_theorem(implies(implies(not(y), not(y)), implies(implies(not(not(y)), not(y)), not(y)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(implies(x, y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 252.19/32.22  = { by axiom 1 (ifeq_axiom) }
% 252.19/32.22    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(implies(not(y), not(y)), implies(implies(not(not(y)), not(y)), not(y))))), true, is_a_theorem(implies(implies(not(y), not(y)), implies(implies(not(not(y)), not(y)), not(y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(implies(x, y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 252.19/32.23  = { by axiom 5 (cn_1) }
% 252.19/32.23    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(y), not(y)), implies(implies(not(not(y)), not(y)), not(y)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(implies(x, y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 252.19/32.23  = { by axiom 1 (ifeq_axiom) }
% 252.19/32.24    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(y), not(y)), implies(implies(not(not(y)), not(y)), not(y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(implies(x, y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 252.19/32.24  = { by axiom 1 (ifeq_axiom) R->L }
% 252.19/32.24    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(y), not(y)), implies(implies(not(not(y)), not(y)), not(y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(implies(x, y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 252.19/32.24  = { by axiom 5 (cn_1) R->L }
% 252.19/32.25    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(y), not(y)), implies(implies(not(not(y)), not(y)), not(y))), implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(implies(x, y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))))), true, ifeq(is_a_theorem(implies(implies(not(y), not(y)), implies(implies(not(not(y)), not(y)), not(y)))), true, is_a_theorem(implies(implies(implies(implies(not(not(y)), not(y)), not(y)), implies(not(implies(x, y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 252.19/32.25  = { by axiom 4 (condensed_detachment) }
% 252.19/32.25    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 252.19/32.26  = { by axiom 1 (ifeq_axiom) }
% 252.19/32.26    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 252.19/32.26  = { by axiom 1 (ifeq_axiom) R->L }
% 252.19/32.26    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 252.19/32.27  = { by axiom 4 (condensed_detachment) R->L }
% 252.19/32.27    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y)))), implies(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))))), true, ifeq(is_a_theorem(implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y))))), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 252.19/32.27  = { by axiom 5 (cn_1) }
% 252.19/32.28    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y))))), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 252.19/32.28  = { by axiom 1 (ifeq_axiom) }
% 252.19/32.28    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y))))), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 252.19/32.29  = { by axiom 1 (ifeq_axiom) R->L }
% 252.19/32.29    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 252.19/32.29  = { by axiom 4 (condensed_detachment) R->L }
% 252.19/32.30    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(y), implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y)))), implies(implies(implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))), implies(not(implies(x, y)), implies(not(not(y)), not(y)))), implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y))))))), true, ifeq(is_a_theorem(implies(not(y), implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))), implies(not(implies(x, y)), implies(not(not(y)), not(y)))), implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y)))))), true), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 252.19/32.30  = { by axiom 5 (cn_1) }
% 252.19/32.30    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(y), implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))), implies(not(implies(x, y)), implies(not(not(y)), not(y)))), implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y)))))), true), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 252.19/32.31  = { by axiom 1 (ifeq_axiom) }
% 252.19/32.31    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(y), implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))), implies(not(implies(x, y)), implies(not(not(y)), not(y)))), implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 252.19/32.32  = { by axiom 1 (ifeq_axiom) R->L }
% 253.04/32.32    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(y), implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))), implies(not(implies(x, y)), implies(not(not(y)), not(y)))), implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 253.04/32.33  = { by axiom 5 (cn_1) R->L }
% 253.04/32.33    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(y)), not(not(implies(x, y)))), implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))), implies(not(implies(x, y)), implies(not(not(y)), not(y)))), implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 253.04/32.33  = { by axiom 1 (ifeq_axiom) R->L }
% 253.04/32.34    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(y)), not(not(implies(x, y)))), implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))), implies(not(implies(x, y)), implies(not(not(y)), not(y)))), implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 253.04/32.34  = { by axiom 4 (condensed_detachment) R->L }
% 253.04/32.35    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(y), implies(not(not(y)), not(not(implies(x, y))))), implies(implies(implies(not(not(y)), not(not(implies(x, y)))), implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y)))), implies(not(y), implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))))))), true, ifeq(is_a_theorem(implies(not(y), implies(not(not(y)), not(not(implies(x, y)))))), true, is_a_theorem(implies(implies(implies(not(not(y)), not(not(implies(x, y)))), implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y)))), implies(not(y), implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(y)), not(not(implies(x, y)))), implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))), implies(not(implies(x, y)), implies(not(not(y)), not(y)))), implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 253.04/32.35  = { by axiom 2 (cn_3) }
% 253.04/32.36    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(y), implies(not(not(y)), not(not(implies(x, y))))), implies(implies(implies(not(not(y)), not(not(implies(x, y)))), implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y)))), implies(not(y), implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(y)), not(not(implies(x, y)))), implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y)))), implies(not(y), implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(y)), not(not(implies(x, y)))), implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))), implies(not(implies(x, y)), implies(not(not(y)), not(y)))), implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 253.04/32.36  = { by axiom 1 (ifeq_axiom) }
% 253.04/32.36    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(y), implies(not(not(y)), not(not(implies(x, y))))), implies(implies(implies(not(not(y)), not(not(implies(x, y)))), implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y)))), implies(not(y), implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))))))), true, is_a_theorem(implies(implies(implies(not(not(y)), not(not(implies(x, y)))), implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y)))), implies(not(y), implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(y)), not(not(implies(x, y)))), implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))), implies(not(implies(x, y)), implies(not(not(y)), not(y)))), implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 253.04/32.37  = { by axiom 5 (cn_1) }
% 253.04/32.37    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(y)), not(not(implies(x, y)))), implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y)))), implies(not(y), implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(y)), not(not(implies(x, y)))), implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))), implies(not(implies(x, y)), implies(not(not(y)), not(y)))), implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 253.04/32.38  = { by axiom 1 (ifeq_axiom) }
% 253.04/32.38    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(y)), not(not(implies(x, y)))), implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y)))), implies(not(y), implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y)))))), true, ifeq(is_a_theorem(implies(implies(not(not(y)), not(not(implies(x, y)))), implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))), implies(not(implies(x, y)), implies(not(not(y)), not(y)))), implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 253.04/32.38  = { by axiom 4 (condensed_detachment) }
% 253.04/32.39    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(implies(x, y))), not(y)), implies(not(not(y)), not(y))), implies(not(implies(x, y)), implies(not(not(y)), not(y)))), implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 253.04/32.39  = { by axiom 1 (ifeq_axiom) }
% 253.04/32.40    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))), implies(not(implies(x, y)), implies(not(not(y)), not(y)))), implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y)))))), true, is_a_theorem(implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 253.72/32.41  = { by axiom 1 (ifeq_axiom) R->L }
% 253.72/32.41    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))), implies(not(implies(x, y)), implies(not(not(y)), not(y)))), implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y)))))), true, ifeq(true, true, is_a_theorem(implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 253.72/32.42  = { by axiom 4 (condensed_detachment) R->L }
% 253.72/32.42    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))), implies(not(implies(x, y)), implies(not(not(y)), not(y)))), implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(implies(x, y))), not(y))), implies(implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))), implies(not(implies(x, y)), implies(not(not(y)), not(y)))))), true, ifeq(is_a_theorem(implies(not(implies(x, y)), implies(not(not(implies(x, y))), not(y)))), true, is_a_theorem(implies(implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))), implies(not(implies(x, y)), implies(not(not(y)), not(y))))), true), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 253.72/32.43  = { by axiom 2 (cn_3) }
% 253.72/32.43    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))), implies(not(implies(x, y)), implies(not(not(y)), not(y)))), implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(implies(x, y))), not(y))), implies(implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))), implies(not(implies(x, y)), implies(not(not(y)), not(y)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))), implies(not(implies(x, y)), implies(not(not(y)), not(y))))), true), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 253.72/32.43  = { by axiom 1 (ifeq_axiom) }
% 253.72/32.44    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))), implies(not(implies(x, y)), implies(not(not(y)), not(y)))), implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(implies(x, y))), not(y))), implies(implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))), implies(not(implies(x, y)), implies(not(not(y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))), implies(not(implies(x, y)), implies(not(not(y)), not(y))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 253.72/32.44  = { by axiom 5 (cn_1) }
% 253.72/32.44    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))), implies(not(implies(x, y)), implies(not(not(y)), not(y)))), implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))), implies(not(implies(x, y)), implies(not(not(y)), not(y))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 253.72/32.45  = { by axiom 1 (ifeq_axiom) }
% 253.72/32.45    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))), implies(not(implies(x, y)), implies(not(not(y)), not(y)))), implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y)))))), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, y))), not(y)), implies(not(not(y)), not(y))), implies(not(implies(x, y)), implies(not(not(y)), not(y))))), true, is_a_theorem(implies(not(y), implies(not(implies(x, y)), implies(not(not(y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 253.72/32.45  = { by axiom 4 (condensed_detachment) }
% 253.72/32.46    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 253.72/32.46  = { by axiom 1 (ifeq_axiom) }
% 253.72/32.46    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y)))))), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(y)), not(y))), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(not(y), implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 253.72/32.46  = { by axiom 4 (condensed_detachment) }
% 253.72/32.47    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 253.72/32.47  = { by axiom 1 (ifeq_axiom) }
% 253.72/32.47    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 253.72/32.48  = { by axiom 1 (ifeq_axiom) R->L }
% 253.72/32.48    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 253.72/32.48  = { by axiom 4 (condensed_detachment) R->L }
% 253.72/32.48    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 253.72/32.49  = { by axiom 5 (cn_1) }
% 253.72/32.49    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 253.72/32.49  = { by axiom 1 (ifeq_axiom) }
% 253.72/32.50    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 253.72/32.50  = { by axiom 5 (cn_1) }
% 253.72/32.50    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 254.51/32.50  = { by axiom 1 (ifeq_axiom) }
% 254.51/32.50    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(y), not(y)), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(y), not(y))), implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 254.51/32.51  = { by axiom 4 (condensed_detachment) }
% 254.51/32.51    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 254.51/32.51  = { by axiom 1 (ifeq_axiom) }
% 254.51/32.51    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 254.51/32.51  = { by axiom 1 (ifeq_axiom) R->L }
% 254.51/32.52    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 254.51/32.52  = { by axiom 5 (cn_1) R->L }
% 254.51/32.52    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))))), true, ifeq(is_a_theorem(implies(not(y), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 254.51/32.52  = { by axiom 4 (condensed_detachment) }
% 254.51/32.52    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 254.51/32.52  = { by axiom 1 (ifeq_axiom) }
% 254.51/32.52    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), not(y)), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(not(y), not(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 254.51/32.52  = { by axiom 4 (condensed_detachment) }
% 254.51/32.52    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 254.51/32.52  = { by axiom 1 (ifeq_axiom) }
% 254.51/32.52    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 254.51/32.53  = { by axiom 1 (ifeq_axiom) R->L }
% 254.51/32.53    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 254.51/32.53  = { by axiom 4 (condensed_detachment) R->L }
% 254.51/32.53    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 254.51/32.53  = { by axiom 5 (cn_1) }
% 254.51/32.53    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 254.51/32.53  = { by axiom 1 (ifeq_axiom) }
% 254.51/32.53    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 254.51/32.54  = { by axiom 1 (ifeq_axiom) R->L }
% 254.51/32.54    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 254.51/32.54  = { by axiom 4 (condensed_detachment) R->L }
% 254.51/32.54    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y), implies(not(implies(not(implies(x, y)), not(y))), y)))), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y), implies(not(implies(not(implies(x, y)), not(y))), y))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 254.51/32.54  = { by axiom 2 (cn_3) }
% 254.51/32.54    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y), implies(not(implies(not(implies(x, y)), not(y))), y)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y), implies(not(implies(not(implies(x, y)), not(y))), y))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 254.51/32.54  = { by axiom 1 (ifeq_axiom) }
% 254.51/32.55    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y), implies(not(implies(not(implies(x, y)), not(y))), y)))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y), implies(not(implies(not(implies(x, y)), not(y))), y))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 254.51/32.55  = { by axiom 5 (cn_1) }
% 254.51/32.55    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y), implies(not(implies(not(implies(x, y)), not(y))), y))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 254.51/32.55  = { by axiom 1 (ifeq_axiom) }
% 254.51/32.55    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y), implies(not(implies(not(implies(x, y)), not(y))), y))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 254.51/32.55  = { by axiom 1 (ifeq_axiom) R->L }
% 254.51/32.55    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y), implies(not(implies(not(implies(x, y)), not(y))), y))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 254.51/32.55  = { by axiom 5 (cn_1) R->L }
% 254.51/32.55    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y), implies(not(implies(not(implies(x, y)), not(y))), y)), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y), implies(not(implies(not(implies(x, y)), not(y))), y))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 254.51/32.56  = { by axiom 4 (condensed_detachment) }
% 254.51/32.56    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 254.51/32.56  = { by axiom 1 (ifeq_axiom) }
% 254.51/32.56    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y), implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), not(y)))), not(implies(not(implies(x, y)), not(y)))), y)), true, is_a_theorem(implies(implies(y, implies(x, y)), implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)))), true), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 254.51/32.56  = { by axiom 4 (condensed_detachment) }
% 254.51/32.56    ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 254.51/32.56  = { by axiom 1 (ifeq_axiom) }
% 254.51/32.56    ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true)
% 254.51/32.56  = { by axiom 1 (ifeq_axiom) R->L }
% 254.51/32.56    ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 254.51/32.56  = { by axiom 4 (condensed_detachment) R->L }
% 254.51/32.56    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))), implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 254.51/32.56  = { by axiom 1 (ifeq_axiom) R->L }
% 254.51/32.56    ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))), implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 254.51/32.56  = { by axiom 5 (cn_1) R->L }
% 254.51/32.56    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))), implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 254.51/32.56  = { by axiom 1 (ifeq_axiom) R->L }
% 254.51/32.56    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))), implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 254.51/32.56  = { by axiom 5 (cn_1) R->L }
% 254.51/32.57    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))), implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))), implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 254.51/32.57  = { by axiom 4 (condensed_detachment) }
% 254.51/32.57    ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 254.51/32.57  = { by axiom 1 (ifeq_axiom) }
% 254.51/32.57    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 254.51/32.57  = { by axiom 1 (ifeq_axiom) R->L }
% 254.51/32.57    ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 254.51/32.58  = { by axiom 4 (condensed_detachment) R->L }
% 254.51/32.58    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 254.51/32.58  = { by axiom 1 (ifeq_axiom) R->L }
% 254.51/32.58    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 254.51/32.59  = { by axiom 4 (condensed_detachment) R->L }
% 254.51/32.59    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 254.51/32.60  = { by axiom 5 (cn_1) }
% 254.51/32.60    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 254.51/32.61  = { by axiom 1 (ifeq_axiom) }
% 255.33/32.61    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 255.33/32.62  = { by axiom 1 (ifeq_axiom) R->L }
% 255.33/32.62    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 255.33/32.62  = { by axiom 5 (cn_1) R->L }
% 255.33/32.63    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 255.33/32.63  = { by axiom 1 (ifeq_axiom) R->L }
% 255.33/32.63    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 255.33/32.64  = { by axiom 3 (cn_2) R->L }
% 255.33/32.64    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 255.33/32.65  = { by axiom 4 (condensed_detachment) }
% 255.33/32.65    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 255.33/32.66  = { by axiom 1 (ifeq_axiom) }
% 255.33/32.66    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 255.33/32.67  = { by axiom 1 (ifeq_axiom) R->L }
% 255.33/32.67    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 255.33/32.67  = { by axiom 4 (condensed_detachment) R->L }
% 255.33/32.68    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 255.33/32.69  = { by axiom 5 (cn_1) }
% 255.33/32.69    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 255.33/32.70  = { by axiom 1 (ifeq_axiom) }
% 256.11/32.70    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 256.11/32.71  = { by axiom 5 (cn_1) }
% 256.11/32.71    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 256.11/32.71  = { by axiom 1 (ifeq_axiom) }
% 256.11/32.72    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 256.11/32.72  = { by axiom 4 (condensed_detachment) }
% 256.11/32.72    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 256.11/32.72  = { by axiom 1 (ifeq_axiom) }
% 256.11/32.72    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 256.11/32.73  = { by axiom 1 (ifeq_axiom) R->L }
% 256.11/32.73    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 256.11/32.73  = { by axiom 4 (condensed_detachment) R->L }
% 256.11/32.73    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 256.11/32.74  = { by axiom 2 (cn_3) }
% 256.11/32.74    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 256.11/32.74  = { by axiom 1 (ifeq_axiom) }
% 256.11/32.75    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 256.11/32.75  = { by axiom 1 (ifeq_axiom) R->L }
% 256.11/32.75    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 256.11/32.75  = { by axiom 4 (condensed_detachment) R->L }
% 256.11/32.76    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true, ifeq(is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 256.11/32.76  = { by axiom 5 (cn_1) }
% 256.11/32.76    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 256.11/32.77  = { by axiom 1 (ifeq_axiom) }
% 256.11/32.77    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 256.11/32.78  = { by axiom 1 (ifeq_axiom) R->L }
% 256.11/32.78    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 256.11/32.78  = { by axiom 4 (condensed_detachment) R->L }
% 256.11/32.79    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), implies(implies(not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y))))))), true, ifeq(is_a_theorem(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 256.11/32.79  = { by axiom 5 (cn_1) }
% 256.11/32.80    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 256.11/32.80  = { by axiom 1 (ifeq_axiom) }
% 256.92/32.81    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 256.92/32.81  = { by axiom 1 (ifeq_axiom) R->L }
% 256.92/32.82    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 256.92/32.82  = { by axiom 2 (cn_3) R->L }
% 256.92/32.82    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), true, is_a_theorem(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 256.92/32.83  = { by axiom 1 (ifeq_axiom) R->L }
% 256.92/32.83    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), true, is_a_theorem(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 256.92/32.84  = { by axiom 2 (cn_3) R->L }
% 256.92/32.84    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))))), true, ifeq(is_a_theorem(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), true, is_a_theorem(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 256.92/32.84  = { by axiom 4 (condensed_detachment) }
% 256.92/32.85    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 256.92/32.85  = { by axiom 1 (ifeq_axiom) }
% 256.92/32.86    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 256.92/32.87  = { by axiom 1 (ifeq_axiom) R->L }
% 256.92/32.87    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 256.92/32.88  = { by axiom 4 (condensed_detachment) R->L }
% 256.92/32.88    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(x, y), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y))))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))))), true, ifeq(is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y))))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 256.92/32.89  = { by axiom 2 (cn_3) }
% 256.92/32.89    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(x, y), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y))))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y))))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 256.92/32.90  = { by axiom 1 (ifeq_axiom) }
% 256.92/32.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(x, y), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y))))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y))))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 257.69/32.90  = { by axiom 5 (cn_1) }
% 257.69/32.91    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y))))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 257.69/32.91  = { by axiom 1 (ifeq_axiom) }
% 257.69/32.92    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y))))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y))))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 257.69/32.92  = { by axiom 4 (condensed_detachment) }
% 257.69/32.93    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 257.69/32.94  = { by axiom 1 (ifeq_axiom) }
% 257.69/32.94    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 257.69/32.95  = { by axiom 1 (ifeq_axiom) R->L }
% 257.69/32.95    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 257.69/32.97  = { by axiom 4 (condensed_detachment) R->L }
% 257.69/32.98    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), 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% 257.69/33.00  = { by axiom 1 (ifeq_axiom) R->L }
% 258.50/33.01    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), 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% 258.50/33.03  = { by axiom 5 (cn_1) R->L }
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% 258.50/33.05  = { by axiom 1 (ifeq_axiom) R->L }
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% 258.50/33.09  = { by axiom 5 (cn_1) R->L }
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% 259.30/33.11  = { by axiom 4 (condensed_detachment) }
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implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), 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implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 259.30/33.13  = { by axiom 1 (ifeq_axiom) }
% 259.30/33.14    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 259.30/33.15  = { by axiom 1 (ifeq_axiom) R->L }
% 259.30/33.16    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 259.30/33.17  = { by axiom 4 (condensed_detachment) R->L }
% 259.30/33.18    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), 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not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, 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% 259.30/33.18  = { by axiom 3 (cn_2) }
% 259.30/33.19    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), 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% 259.30/33.20  = { by axiom 1 (ifeq_axiom) }
% 259.30/33.21    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), 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implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 259.30/33.22  = { by axiom 5 (cn_1) }
% 259.30/33.23    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 259.30/33.24  = { by axiom 1 (ifeq_axiom) }
% 259.30/33.24    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 259.30/33.25  = { by axiom 1 (ifeq_axiom) R->L }
% 259.30/33.26    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 259.30/33.26  = { by axiom 5 (cn_1) R->L }
% 259.30/33.27    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 259.30/33.27  = { by axiom 4 (condensed_detachment) }
% 259.30/33.28    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 259.30/33.28  = { by axiom 1 (ifeq_axiom) }
% 259.30/33.28    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 259.30/33.29  = { by axiom 4 (condensed_detachment) }
% 259.30/33.29    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 259.30/33.29  = { by axiom 1 (ifeq_axiom) }
% 259.30/33.29    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 259.30/33.30  = { by axiom 1 (ifeq_axiom) R->L }
% 259.30/33.30    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 259.30/33.30  = { by axiom 4 (condensed_detachment) R->L }
% 259.30/33.30    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 259.30/33.31  = { by axiom 5 (cn_1) }
% 259.30/33.31    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 259.30/33.31  = { by axiom 1 (ifeq_axiom) }
% 259.30/33.32    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 260.88/33.32  = { by axiom 1 (ifeq_axiom) R->L }
% 260.88/33.32    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 260.88/33.33  = { by axiom 5 (cn_1) R->L }
% 260.88/33.33    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 260.88/33.33  = { by axiom 1 (ifeq_axiom) R->L }
% 260.88/33.34    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 260.88/33.34  = { by axiom 3 (cn_2) R->L }
% 260.88/33.34    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 260.88/33.34  = { by axiom 4 (condensed_detachment) }
% 260.88/33.35    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 260.88/33.35  = { by axiom 1 (ifeq_axiom) }
% 260.88/33.35    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(implies(x, y), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 260.88/33.35  = { by axiom 4 (condensed_detachment) }
% 260.88/33.35    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 260.88/33.35  = { by axiom 1 (ifeq_axiom) }
% 260.88/33.35    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 260.88/33.35  = { by axiom 1 (ifeq_axiom) R->L }
% 260.88/33.35    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 260.88/33.35  = { by axiom 3 (cn_2) R->L }
% 260.88/33.35    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y))))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), not(y))), implies(not(implies(not(implies(x, y)), not(y))), implies(not(implies(x, y)), not(y)))), implies(not(implies(x, y)), not(y)))), true), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 260.88/33.35  = { by axiom 4 (condensed_detachment) }
% 260.88/33.35    ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 260.88/33.35  = { by axiom 1 (ifeq_axiom) }
% 260.88/33.35    ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y)), implies(not(implies(x, y)), not(y)))), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), not(y))), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), not(y))), true), true)
% 260.88/33.36  = { by axiom 4 (condensed_detachment) }
% 260.88/33.36    true
% 260.88/33.36  % SZS output end Proof
% 260.88/33.36  
% 260.88/33.36  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------