Twee---2.7.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : LCL034-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n002.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Sep 29 11:48:52 AM UTC 2026

% Result   : Unsatisfiable 7.49s 1.47s
% Output   : Proof 201.35s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : LCL034-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04  % Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36  % Computer : n002.cluster.edu
% 0.08/0.36  % Model    : x86_64 x86_64
% 0.08/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36  % Memory   : 8046.5625MB
% 0.08/0.36  % OS       : Linux 6.8.0-71-generic
% 0.08/0.36  % CPULimit : 300
% 0.08/0.36  % WCLimit  : 300
% 0.08/0.36  % DateTime : Sun Sep 27 15:20:51 UTC 2026
% 0.08/0.37  % CPUTime  : 
% 0.08/0.37  Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.49/1.47  Command-line arguments: --no-flatten-goal
% 7.49/1.47  
% 7.49/1.47  % SZS status Unsatisfiable
% 7.49/1.47  
% 184.08/26.78  % SZS output start Proof
% 184.08/26.78  Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 184.08/26.78  Axiom 2 (condensed_detachment): ifeq(is_a_theorem(implies(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 186.40/27.06  Axiom 3 (c0_CAMeredith): is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X)))) = true.
% 186.40/27.06  
% 186.40/27.06  Goal 1 (prove_c0_3): is_a_theorem(implies(implies(implies(a, b), a), a)) = true.
% 186.40/27.06  Proof:
% 186.40/27.06    is_a_theorem(implies(implies(implies(a, b), a), a))
% 186.40/27.06  = { by axiom 1 (ifeq_axiom) R->L }
% 186.40/27.06    ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 186.40/27.06  = { by axiom 2 (condensed_detachment) R->L }
% 186.40/27.06    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 186.40/27.06  = { by axiom 1 (ifeq_axiom) R->L }
% 186.40/27.06    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 186.40/27.06  = { by axiom 2 (condensed_detachment) R->L }
% 186.40/27.07    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood))), implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 186.40/27.07  = { by axiom 3 (c0_CAMeredith) }
% 186.40/27.07    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 186.40/27.07  = { by axiom 1 (ifeq_axiom) }
% 186.40/27.07    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 186.40/27.07  = { by axiom 1 (ifeq_axiom) R->L }
% 186.40/27.07    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 186.40/27.07  = { by axiom 2 (condensed_detachment) R->L }
% 186.40/27.07    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 186.40/27.07  = { by axiom 3 (c0_CAMeredith) }
% 186.40/27.08    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 186.40/27.08  = { by axiom 1 (ifeq_axiom) }
% 186.40/27.08    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 186.40/27.08  = { by axiom 1 (ifeq_axiom) R->L }
% 186.40/27.08    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 186.40/27.08  = { by axiom 2 (condensed_detachment) R->L }
% 186.40/27.09    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 186.40/27.09  = { by axiom 3 (c0_CAMeredith) }
% 186.40/27.09    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 186.40/27.09  = { by axiom 1 (ifeq_axiom) }
% 186.40/27.09    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 186.40/27.10  = { by axiom 1 (ifeq_axiom) R->L }
% 186.40/27.10    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 186.40/27.10  = { by axiom 2 (condensed_detachment) R->L }
% 186.40/27.11    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true, ifeq(is_a_theorem(implies(falsehood, implies(T, S))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 186.40/27.11  = { by axiom 1 (ifeq_axiom) R->L }
% 186.40/27.11    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(falsehood, implies(T, S))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 186.40/27.11  = { by axiom 2 (condensed_detachment) R->L }
% 186.40/27.12    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(S, falsehood), implies(T, falsehood)), implies(falsehood, X2)), implies(Y2, implies(falsehood, X2))), implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(S, falsehood), implies(T, falsehood)), implies(falsehood, X2)), implies(Y2, implies(falsehood, X2)))), true, is_a_theorem(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S))), true), true), true, is_a_theorem(implies(falsehood, implies(T, S))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 186.40/27.12  = { by axiom 3 (c0_CAMeredith) }
% 186.40/27.12    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(S, falsehood), implies(T, falsehood)), implies(falsehood, X2)), implies(Y2, implies(falsehood, X2)))), true, is_a_theorem(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S))), true), true), true, is_a_theorem(implies(falsehood, implies(T, S))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 186.40/27.13  = { by axiom 1 (ifeq_axiom) }
% 187.11/27.13    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S, falsehood), implies(T, falsehood)), implies(falsehood, X2)), implies(Y2, implies(falsehood, X2)))), true, is_a_theorem(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S))), true), true, is_a_theorem(implies(falsehood, implies(T, S))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 187.11/27.13  = { by axiom 1 (ifeq_axiom) R->L }
% 187.11/27.14    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S, falsehood), implies(T, falsehood)), implies(falsehood, X2)), implies(Y2, implies(falsehood, X2)))), true), true, is_a_theorem(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S))), true), true, is_a_theorem(implies(falsehood, implies(T, S))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 187.11/27.14  = { by axiom 3 (c0_CAMeredith) R->L }
% 187.11/27.14    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, X2), implies(T, falsehood)), implies(Y2, falsehood)), S), implies(implies(S, falsehood), implies(T, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(S, falsehood), implies(T, falsehood)), implies(falsehood, X2)), implies(Y2, implies(falsehood, X2)))), true), true, is_a_theorem(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S))), true), true, is_a_theorem(implies(falsehood, implies(T, S))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 187.11/27.15  = { by axiom 1 (ifeq_axiom) R->L }
% 187.11/27.15    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, X2), implies(T, falsehood)), implies(Y2, falsehood)), S), implies(implies(S, falsehood), implies(T, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(S, falsehood), implies(T, falsehood)), implies(falsehood, X2)), implies(Y2, implies(falsehood, X2)))), true), true), true, is_a_theorem(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S))), true), true, is_a_theorem(implies(falsehood, implies(T, S))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 187.11/27.15  = { by axiom 3 (c0_CAMeredith) R->L }
% 187.11/27.16    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, X2), implies(T, falsehood)), implies(Y2, falsehood)), S), implies(implies(S, falsehood), implies(T, falsehood))), implies(implies(implies(implies(S, falsehood), implies(T, falsehood)), implies(falsehood, X2)), implies(Y2, implies(falsehood, X2))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, X2), implies(T, falsehood)), implies(Y2, falsehood)), S), implies(implies(S, falsehood), implies(T, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(S, falsehood), implies(T, falsehood)), implies(falsehood, X2)), implies(Y2, implies(falsehood, X2)))), true), true), true, is_a_theorem(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S))), true), true, is_a_theorem(implies(falsehood, implies(T, S))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 187.11/27.16  = { by axiom 2 (condensed_detachment) }
% 187.11/27.16    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S))), true), true, is_a_theorem(implies(falsehood, implies(T, S))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 187.11/27.17  = { by axiom 1 (ifeq_axiom) }
% 187.11/27.17    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S))), true, is_a_theorem(implies(falsehood, implies(T, S))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 187.11/27.17  = { by axiom 1 (ifeq_axiom) R->L }
% 187.11/27.18    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S))), true, is_a_theorem(implies(falsehood, implies(T, S))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 187.11/27.18  = { by axiom 2 (condensed_detachment) R->L }
% 187.11/27.18    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(T, S), Z2), implies(falsehood, falsehood)), S), implies(implies(Y2, implies(falsehood, X2)), S)), implies(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S)), implies(falsehood, implies(T, S))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(T, S), Z2), implies(falsehood, falsehood)), S), implies(implies(Y2, implies(falsehood, X2)), S))), true, is_a_theorem(implies(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S)), implies(falsehood, implies(T, S)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S))), true, is_a_theorem(implies(falsehood, implies(T, S))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 187.11/27.19  = { by axiom 3 (c0_CAMeredith) }
% 187.11/27.19    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(T, S), Z2), implies(falsehood, falsehood)), S), implies(implies(Y2, implies(falsehood, X2)), S))), true, is_a_theorem(implies(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S)), implies(falsehood, implies(T, S)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S))), true, is_a_theorem(implies(falsehood, implies(T, S))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 187.11/27.20  = { by axiom 1 (ifeq_axiom) }
% 187.56/27.20    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T, S), Z2), implies(falsehood, falsehood)), S), implies(implies(Y2, implies(falsehood, X2)), S))), true, is_a_theorem(implies(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S)), implies(falsehood, implies(T, S)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S))), true, is_a_theorem(implies(falsehood, implies(T, S))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 187.56/27.20  = { by axiom 1 (ifeq_axiom) R->L }
% 187.56/27.21    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(T, S), Z2), implies(falsehood, falsehood)), S), implies(implies(Y2, implies(falsehood, X2)), S))), true), true, is_a_theorem(implies(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S)), implies(falsehood, implies(T, S)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S))), true, is_a_theorem(implies(falsehood, implies(T, S))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 187.56/27.21  = { by axiom 2 (condensed_detachment) R->L }
% 187.56/27.21    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(Y2, implies(falsehood, X2)), falsehood)), implies(implies(implies(T, S), Z2), falsehood)), S), implies(implies(S, falsehood), implies(implies(Y2, implies(falsehood, X2)), falsehood))), implies(implies(implies(implies(S, falsehood), implies(implies(Y2, implies(falsehood, X2)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(T, S), Z2), implies(falsehood, falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(Y2, implies(falsehood, X2)), falsehood)), implies(implies(implies(T, S), Z2), falsehood)), S), implies(implies(S, falsehood), implies(implies(Y2, implies(falsehood, X2)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(S, falsehood), implies(implies(Y2, implies(falsehood, X2)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(T, S), Z2), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(T, S), Z2), implies(falsehood, falsehood)), S), implies(implies(Y2, implies(falsehood, X2)), S))), true), true, is_a_theorem(implies(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S)), implies(falsehood, implies(T, S)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S))), true, is_a_theorem(implies(falsehood, implies(T, S))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 187.56/27.22  = { by axiom 3 (c0_CAMeredith) }
% 187.56/27.22    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(Y2, implies(falsehood, X2)), falsehood)), implies(implies(implies(T, S), Z2), falsehood)), S), implies(implies(S, falsehood), implies(implies(Y2, implies(falsehood, X2)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(S, falsehood), implies(implies(Y2, implies(falsehood, X2)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(T, S), Z2), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(T, S), Z2), implies(falsehood, falsehood)), S), implies(implies(Y2, implies(falsehood, X2)), S))), true), true, is_a_theorem(implies(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S)), implies(falsehood, implies(T, S)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S))), true, is_a_theorem(implies(falsehood, implies(T, S))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 187.56/27.23  = { by axiom 1 (ifeq_axiom) }
% 187.56/27.23    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(Y2, implies(falsehood, X2)), falsehood)), implies(implies(implies(T, S), Z2), falsehood)), S), implies(implies(S, falsehood), implies(implies(Y2, implies(falsehood, X2)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(S, falsehood), implies(implies(Y2, implies(falsehood, X2)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(T, S), Z2), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(T, S), Z2), implies(falsehood, falsehood)), S), implies(implies(Y2, implies(falsehood, X2)), S))), true), true, is_a_theorem(implies(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S)), implies(falsehood, implies(T, S)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S))), true, is_a_theorem(implies(falsehood, implies(T, S))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 187.56/27.23  = { by axiom 3 (c0_CAMeredith) }
% 187.56/27.24    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S, falsehood), implies(implies(Y2, implies(falsehood, X2)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(T, S), Z2), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(T, S), Z2), implies(falsehood, falsehood)), S), implies(implies(Y2, implies(falsehood, X2)), S))), true), true, is_a_theorem(implies(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S)), implies(falsehood, implies(T, S)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S))), true, is_a_theorem(implies(falsehood, implies(T, S))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 187.56/27.24  = { by axiom 1 (ifeq_axiom) }
% 187.56/27.24    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S, falsehood), implies(implies(Y2, implies(falsehood, X2)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(T, S), Z2), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(T, S), Z2), implies(falsehood, falsehood)), S), implies(implies(Y2, implies(falsehood, X2)), S))), true), true, is_a_theorem(implies(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S)), implies(falsehood, implies(T, S)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S))), true, is_a_theorem(implies(falsehood, implies(T, S))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 187.56/27.25  = { by axiom 1 (ifeq_axiom) R->L }
% 187.56/27.25    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(S, falsehood), implies(implies(Y2, implies(falsehood, X2)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(T, S), Z2), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(T, S), Z2), implies(falsehood, falsehood)), S), implies(implies(Y2, implies(falsehood, X2)), S))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S)), implies(falsehood, implies(T, S)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S))), true, is_a_theorem(implies(falsehood, implies(T, S))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 187.56/27.25  = { by axiom 3 (c0_CAMeredith) R->L }
% 187.56/27.26    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(S, falsehood), implies(implies(Y2, implies(falsehood, X2)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(T, S), Z2), implies(falsehood, falsehood))), implies(implies(implies(implies(implies(T, S), Z2), implies(falsehood, falsehood)), S), implies(implies(Y2, implies(falsehood, X2)), S)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(S, falsehood), implies(implies(Y2, implies(falsehood, X2)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(T, S), Z2), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(T, S), Z2), implies(falsehood, falsehood)), S), implies(implies(Y2, implies(falsehood, X2)), S))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S)), implies(falsehood, implies(T, S)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S))), true, is_a_theorem(implies(falsehood, implies(T, S))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 187.56/27.26  = { by axiom 2 (condensed_detachment) }
% 187.56/27.26    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S)), implies(falsehood, implies(T, S)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S))), true, is_a_theorem(implies(falsehood, implies(T, S))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 187.56/27.27  = { by axiom 1 (ifeq_axiom) }
% 187.56/27.27    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S)), implies(falsehood, implies(T, S)))), true, ifeq(is_a_theorem(implies(implies(implies(Y2, implies(falsehood, X2)), S), implies(T, S))), true, is_a_theorem(implies(falsehood, implies(T, S))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 187.56/27.27  = { by axiom 2 (condensed_detachment) }
% 187.56/27.28    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 187.56/27.28  = { by axiom 1 (ifeq_axiom) }
% 187.56/27.29    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 187.56/27.29  = { by axiom 1 (ifeq_axiom) R->L }
% 187.56/27.29    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 187.56/27.30  = { by axiom 2 (condensed_detachment) R->L }
% 188.30/27.31    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), falsehood)), implies(implies(falsehood, implies(T, S)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), falsehood)), implies(implies(falsehood, implies(T, S)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 188.30/27.31  = { by axiom 3 (c0_CAMeredith) }
% 188.30/27.32    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), falsehood)), implies(implies(falsehood, implies(T, S)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 188.30/27.32  = { by axiom 1 (ifeq_axiom) }
% 188.30/27.33    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), falsehood)), implies(implies(falsehood, implies(T, S)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))))), true), true, is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 188.30/27.34  = { by axiom 3 (c0_CAMeredith) }
% 188.30/27.34    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))))), true), true, is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 188.30/27.35  = { by axiom 1 (ifeq_axiom) }
% 188.30/27.35    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))))), true, is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 188.30/27.36  = { by axiom 1 (ifeq_axiom) R->L }
% 188.30/27.36    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))))), true, ifeq(true, true, is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 188.30/27.37  = { by axiom 2 (condensed_detachment) R->L }
% 188.30/27.38    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 188.30/27.39  = { by axiom 3 (c0_CAMeredith) }
% 189.00/27.40    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 189.00/27.41  = { by axiom 1 (ifeq_axiom) }
% 189.00/27.42    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 189.00/27.43  = { by axiom 1 (ifeq_axiom) R->L }
% 189.00/27.43    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 189.00/27.44  = { by axiom 2 (condensed_detachment) R->L }
% 189.00/27.46    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), V2), implies(falsehood, falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), V2), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), V2), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), V2), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 189.00/27.46  = { by axiom 3 (c0_CAMeredith) }
% 189.00/27.48    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), V2), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), V2), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 189.00/27.49  = { by axiom 1 (ifeq_axiom) }
% 189.00/27.50    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), V2), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), V2), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 189.70/27.51  = { by axiom 1 (ifeq_axiom) R->L }
% 189.70/27.52    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), V2), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), V2), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 189.70/27.53  = { by axiom 3 (c0_CAMeredith) R->L }
% 189.70/27.56    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), V2), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), V2), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), V2), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 189.70/27.57  = { by axiom 1 (ifeq_axiom) R->L }
% 189.70/27.58    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), V2), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), V2), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), V2), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 189.70/27.59  = { by axiom 3 (c0_CAMeredith) R->L }
% 190.41/27.61    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), V2), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), V2), implies(falsehood, falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), V2), falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), V2), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), V2), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 190.41/27.62  = { by axiom 2 (condensed_detachment) }
% 190.41/27.63    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), V2), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 190.41/27.63  = { by axiom 1 (ifeq_axiom) }
% 190.41/27.64    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), V2), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 190.41/27.65  = { by axiom 1 (ifeq_axiom) R->L }
% 190.41/27.66    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), V2), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 190.41/27.66  = { by axiom 3 (c0_CAMeredith) R->L }
% 190.41/27.67    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), V2), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), V2), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), W2), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 190.41/27.67  = { by axiom 2 (condensed_detachment) }
% 190.41/27.68    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 190.41/27.68  = { by axiom 1 (ifeq_axiom) }
% 190.41/27.68    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))))), true, ifeq(is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(falsehood, implies(T, S)), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 190.41/27.69  = { by axiom 2 (condensed_detachment) }
% 190.41/27.69    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 190.41/27.69  = { by axiom 1 (ifeq_axiom) }
% 190.41/27.69    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 190.41/27.69  = { by axiom 1 (ifeq_axiom) R->L }
% 190.41/27.70    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.10/27.70  = { by axiom 3 (c0_CAMeredith) R->L }
% 191.10/27.70    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), U), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), falsehood)), implies(implies(a, falsehood), falsehood)), implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.10/27.70  = { by axiom 2 (condensed_detachment) }
% 191.10/27.71    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.10/27.71  = { by axiom 1 (ifeq_axiom) }
% 191.10/27.71    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.10/27.71  = { by axiom 1 (ifeq_axiom) R->L }
% 191.10/27.71    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.10/27.71  = { by axiom 2 (condensed_detachment) R->L }
% 191.10/27.72    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), U2), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)), W), implies(falsehood, W)), implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), U2), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)), W), implies(falsehood, W))), true, is_a_theorem(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.10/27.72  = { by axiom 3 (c0_CAMeredith) }
% 191.10/27.72    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), U2), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)), W), implies(falsehood, W))), true, is_a_theorem(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.10/27.72  = { by axiom 1 (ifeq_axiom) }
% 191.10/27.72    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), U2), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)), W), implies(falsehood, W))), true, is_a_theorem(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.10/27.73  = { by axiom 1 (ifeq_axiom) R->L }
% 191.10/27.73    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), U2), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)), W), implies(falsehood, W))), true), true, is_a_theorem(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.10/27.73  = { by axiom 2 (condensed_detachment) R->L }
% 191.10/27.73    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood), falsehood), implies(implies(implies(implies(a, falsehood), falsehood), U2), falsehood)), implies(falsehood, falsehood)), implies(implies(W, T2), implies(falsehood, falsehood))), implies(implies(implies(implies(W, T2), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), U2), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood), falsehood), implies(implies(implies(implies(a, falsehood), falsehood), U2), falsehood)), implies(falsehood, falsehood)), implies(implies(W, T2), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(W, T2), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), U2), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), U2), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)), W), implies(falsehood, W))), true), true, is_a_theorem(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.10/27.74  = { by axiom 3 (c0_CAMeredith) }
% 191.10/27.74    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood), falsehood), implies(implies(implies(implies(a, falsehood), falsehood), U2), falsehood)), implies(falsehood, falsehood)), implies(implies(W, T2), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(W, T2), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), U2), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), U2), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)), W), implies(falsehood, W))), true), true, is_a_theorem(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.10/27.74  = { by axiom 1 (ifeq_axiom) }
% 191.10/27.75    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood), falsehood), implies(implies(implies(implies(a, falsehood), falsehood), U2), falsehood)), implies(falsehood, falsehood)), implies(implies(W, T2), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(W, T2), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), U2), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), U2), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)), W), implies(falsehood, W))), true), true, is_a_theorem(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.10/27.75  = { by axiom 1 (ifeq_axiom) R->L }
% 191.10/27.75    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood), falsehood), implies(implies(implies(implies(a, falsehood), falsehood), U2), falsehood)), implies(falsehood, falsehood)), implies(implies(W, T2), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(W, T2), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), U2), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), U2), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)), W), implies(falsehood, W))), true), true, is_a_theorem(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.10/27.75  = { by axiom 3 (c0_CAMeredith) R->L }
% 191.10/27.76    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(a, falsehood), falsehood), U2), falsehood)), implies(implies(W, T2), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood), falsehood), implies(implies(implies(implies(a, falsehood), falsehood), U2), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood), falsehood), implies(implies(implies(implies(a, falsehood), falsehood), U2), falsehood)), implies(falsehood, falsehood)), implies(implies(W, T2), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(W, T2), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), U2), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), U2), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)), W), implies(falsehood, W))), true), true, is_a_theorem(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.10/27.76  = { by axiom 1 (ifeq_axiom) R->L }
% 191.10/27.76    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(a, falsehood), falsehood), U2), falsehood)), implies(implies(W, T2), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood), falsehood), implies(implies(implies(implies(a, falsehood), falsehood), U2), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood), falsehood), implies(implies(implies(implies(a, falsehood), falsehood), U2), falsehood)), implies(falsehood, falsehood)), implies(implies(W, T2), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(W, T2), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), U2), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), U2), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)), W), implies(falsehood, W))), true), true, is_a_theorem(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.10/27.76  = { by axiom 3 (c0_CAMeredith) R->L }
% 191.10/27.77    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(a, falsehood), falsehood), U2), falsehood)), implies(implies(W, T2), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood), falsehood), implies(implies(implies(implies(a, falsehood), falsehood), U2), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood), falsehood), implies(implies(implies(implies(a, falsehood), falsehood), U2), falsehood)), implies(falsehood, falsehood)), implies(implies(W, T2), implies(falsehood, falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(a, falsehood), falsehood), U2), falsehood)), implies(implies(W, T2), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood), falsehood), implies(implies(implies(implies(a, falsehood), falsehood), U2), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood), falsehood), implies(implies(implies(implies(a, falsehood), falsehood), U2), falsehood)), implies(falsehood, falsehood)), implies(implies(W, T2), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(W, T2), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), U2), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), U2), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)), W), implies(falsehood, W))), true), true, is_a_theorem(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.10/27.77  = { by axiom 2 (condensed_detachment) }
% 191.10/27.77    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W, T2), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), U2), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), U2), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)), W), implies(falsehood, W))), true), true, is_a_theorem(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.10/27.78  = { by axiom 1 (ifeq_axiom) }
% 191.10/27.78    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W, T2), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), U2), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), U2), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)), W), implies(falsehood, W))), true), true, is_a_theorem(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.10/27.78  = { by axiom 1 (ifeq_axiom) R->L }
% 191.10/27.78    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(W, T2), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), U2), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), U2), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)), W), implies(falsehood, W))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.10/27.78  = { by axiom 3 (c0_CAMeredith) R->L }
% 191.10/27.79    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(W, T2), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), U2), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood))), implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), U2), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)), W), implies(falsehood, W)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(W, T2), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)), implies(implies(implies(implies(a, falsehood), falsehood), U2), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, falsehood), falsehood), U2), implies(implies(implies(implies(implies(a, b), a), falsehood), V), falsehood)), W), implies(falsehood, W))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.10/27.79  = { by axiom 2 (condensed_detachment) }
% 191.10/27.79    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.10/27.79  = { by axiom 1 (ifeq_axiom) }
% 191.10/27.79    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))), implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(falsehood, W), implies(implies(a, falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), falsehood), implies(implies(b, Z), falsehood)), implies(implies(falsehood, W), falsehood)), implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.10/27.79  = { by axiom 2 (condensed_detachment) }
% 191.10/27.79    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.10/27.79  = { by axiom 1 (ifeq_axiom) }
% 191.10/27.79    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.10/27.79  = { by axiom 1 (ifeq_axiom) R->L }
% 191.10/27.79    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.10/27.79  = { by axiom 3 (c0_CAMeredith) R->L }
% 191.10/27.80    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood))), implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), falsehood), V), implies(implies(a, falsehood), falsehood)), implies(a, falsehood)), implies(implies(b, Z), implies(a, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(b, Z), implies(a, falsehood)), implies(implies(implies(a, b), a), falsehood)), implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.10/27.80  = { by axiom 2 (condensed_detachment) }
% 191.10/27.80    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.10/27.80  = { by axiom 1 (ifeq_axiom) }
% 191.82/27.80    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.82/27.80  = { by axiom 1 (ifeq_axiom) R->L }
% 191.82/27.80    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.82/27.80  = { by axiom 3 (c0_CAMeredith) R->L }
% 191.82/27.80    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, falsehood), implies(implies(implies(a, b), a), falsehood)), b), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.82/27.80  = { by axiom 2 (condensed_detachment) }
% 191.82/27.80    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, ifeq(true, true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.82/27.80  = { by axiom 1 (ifeq_axiom) }
% 191.82/27.80    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.82/27.80  = { by axiom 1 (ifeq_axiom) R->L }
% 191.82/27.80    ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.82/27.81  = { by axiom 2 (condensed_detachment) R->L }
% 191.82/27.81    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.82/27.81  = { by axiom 1 (ifeq_axiom) R->L }
% 191.82/27.81    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.82/27.81  = { by axiom 2 (condensed_detachment) R->L }
% 191.82/27.82    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a))), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.82/27.82  = { by axiom 3 (c0_CAMeredith) }
% 191.82/27.82    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.82/27.83  = { by axiom 1 (ifeq_axiom) }
% 191.82/27.83    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.82/27.83  = { by axiom 1 (ifeq_axiom) R->L }
% 191.82/27.84    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.82/27.84  = { by axiom 2 (condensed_detachment) R->L }
% 191.82/27.84    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true, ifeq(is_a_theorem(implies(falsehood, implies(Y3, Z3))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.82/27.85  = { by axiom 1 (ifeq_axiom) R->L }
% 191.82/27.85    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(falsehood, implies(Y3, Z3))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.82/27.86  = { by axiom 2 (condensed_detachment) R->L }
% 191.82/27.86    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z3, falsehood), implies(Y3, falsehood)), implies(falsehood, W3)), implies(V3, implies(falsehood, W3))), implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z3, falsehood), implies(Y3, falsehood)), implies(falsehood, W3)), implies(V3, implies(falsehood, W3)))), true, is_a_theorem(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3))), true), true), true, is_a_theorem(implies(falsehood, implies(Y3, Z3))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.82/27.87  = { by axiom 3 (c0_CAMeredith) }
% 191.82/27.87    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Z3, falsehood), implies(Y3, falsehood)), implies(falsehood, W3)), implies(V3, implies(falsehood, W3)))), true, is_a_theorem(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3))), true), true), true, is_a_theorem(implies(falsehood, implies(Y3, Z3))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.82/27.88  = { by axiom 1 (ifeq_axiom) }
% 191.82/27.88    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z3, falsehood), implies(Y3, falsehood)), implies(falsehood, W3)), implies(V3, implies(falsehood, W3)))), true, is_a_theorem(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3))), true), true, is_a_theorem(implies(falsehood, implies(Y3, Z3))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.82/27.89  = { by axiom 1 (ifeq_axiom) R->L }
% 191.82/27.89    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z3, falsehood), implies(Y3, falsehood)), implies(falsehood, W3)), implies(V3, implies(falsehood, W3)))), true), true, is_a_theorem(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3))), true), true, is_a_theorem(implies(falsehood, implies(Y3, Z3))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.82/27.89  = { by axiom 3 (c0_CAMeredith) R->L }
% 192.53/27.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, W3), implies(Y3, falsehood)), implies(V3, falsehood)), Z3), implies(implies(Z3, falsehood), implies(Y3, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Z3, falsehood), implies(Y3, falsehood)), implies(falsehood, W3)), implies(V3, implies(falsehood, W3)))), true), true, is_a_theorem(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3))), true), true, is_a_theorem(implies(falsehood, implies(Y3, Z3))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 192.53/27.90  = { by axiom 1 (ifeq_axiom) R->L }
% 192.53/27.91    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, W3), implies(Y3, falsehood)), implies(V3, falsehood)), Z3), implies(implies(Z3, falsehood), implies(Y3, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Z3, falsehood), implies(Y3, falsehood)), implies(falsehood, W3)), implies(V3, implies(falsehood, W3)))), true), true), true, is_a_theorem(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3))), true), true, is_a_theorem(implies(falsehood, implies(Y3, Z3))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 192.53/27.91  = { by axiom 3 (c0_CAMeredith) R->L }
% 192.53/27.92    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, W3), implies(Y3, falsehood)), implies(V3, falsehood)), Z3), implies(implies(Z3, falsehood), implies(Y3, falsehood))), implies(implies(implies(implies(Z3, falsehood), implies(Y3, falsehood)), implies(falsehood, W3)), implies(V3, implies(falsehood, W3))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, W3), implies(Y3, falsehood)), implies(V3, falsehood)), Z3), implies(implies(Z3, falsehood), implies(Y3, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Z3, falsehood), implies(Y3, falsehood)), implies(falsehood, W3)), implies(V3, implies(falsehood, W3)))), true), true), true, is_a_theorem(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3))), true), true, is_a_theorem(implies(falsehood, implies(Y3, Z3))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 192.53/27.92  = { by axiom 2 (condensed_detachment) }
% 192.53/27.93    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3))), true), true, is_a_theorem(implies(falsehood, implies(Y3, Z3))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 192.53/27.93  = { by axiom 1 (ifeq_axiom) }
% 192.53/27.94    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3))), true, is_a_theorem(implies(falsehood, implies(Y3, Z3))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 192.53/27.94  = { by axiom 1 (ifeq_axiom) R->L }
% 192.53/27.94    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3))), true, is_a_theorem(implies(falsehood, implies(Y3, Z3))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 192.53/27.95  = { by axiom 2 (condensed_detachment) R->L }
% 192.53/27.95    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(Y3, Z3), U3), implies(falsehood, falsehood)), Z3), implies(implies(V3, implies(falsehood, W3)), Z3)), implies(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3)), implies(falsehood, implies(Y3, Z3))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(Y3, Z3), U3), implies(falsehood, falsehood)), Z3), implies(implies(V3, implies(falsehood, W3)), Z3))), true, is_a_theorem(implies(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3)), implies(falsehood, implies(Y3, Z3)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3))), true, is_a_theorem(implies(falsehood, implies(Y3, Z3))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 192.53/27.96  = { by axiom 3 (c0_CAMeredith) }
% 192.53/27.96    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(Y3, Z3), U3), implies(falsehood, falsehood)), Z3), implies(implies(V3, implies(falsehood, W3)), Z3))), true, is_a_theorem(implies(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3)), implies(falsehood, implies(Y3, Z3)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3))), true, is_a_theorem(implies(falsehood, implies(Y3, Z3))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 192.53/27.97  = { by axiom 1 (ifeq_axiom) }
% 192.53/27.97    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Y3, Z3), U3), implies(falsehood, falsehood)), Z3), implies(implies(V3, implies(falsehood, W3)), Z3))), true, is_a_theorem(implies(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3)), implies(falsehood, implies(Y3, Z3)))), true), true, ifeq(is_a_theorem(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3))), true, is_a_theorem(implies(falsehood, implies(Y3, Z3))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 192.53/27.98  = { by axiom 1 (ifeq_axiom) R->L }
% 192.53/27.98    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(Y3, Z3), U3), implies(falsehood, falsehood)), Z3), implies(implies(V3, implies(falsehood, W3)), Z3))), true), true, is_a_theorem(implies(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3)), implies(falsehood, implies(Y3, Z3)))), true), true, ifeq(is_a_theorem(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3))), true, is_a_theorem(implies(falsehood, implies(Y3, Z3))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 192.53/27.99  = { by axiom 2 (condensed_detachment) R->L }
% 192.53/27.99    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(V3, implies(falsehood, W3)), falsehood)), implies(implies(implies(Y3, Z3), U3), falsehood)), Z3), implies(implies(Z3, falsehood), implies(implies(V3, implies(falsehood, W3)), falsehood))), implies(implies(implies(implies(Z3, falsehood), implies(implies(V3, implies(falsehood, W3)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Y3, Z3), U3), implies(falsehood, falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(V3, implies(falsehood, W3)), falsehood)), implies(implies(implies(Y3, Z3), U3), falsehood)), Z3), implies(implies(Z3, falsehood), implies(implies(V3, implies(falsehood, W3)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Z3, falsehood), implies(implies(V3, implies(falsehood, W3)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Y3, Z3), U3), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(Y3, Z3), U3), implies(falsehood, falsehood)), Z3), implies(implies(V3, implies(falsehood, W3)), Z3))), true), true, is_a_theorem(implies(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3)), implies(falsehood, implies(Y3, Z3)))), true), true, ifeq(is_a_theorem(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3))), true, is_a_theorem(implies(falsehood, implies(Y3, Z3))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 192.53/28.00  = { by axiom 3 (c0_CAMeredith) }
% 192.53/28.00    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(V3, implies(falsehood, W3)), falsehood)), implies(implies(implies(Y3, Z3), U3), falsehood)), Z3), implies(implies(Z3, falsehood), implies(implies(V3, implies(falsehood, W3)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Z3, falsehood), implies(implies(V3, implies(falsehood, W3)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Y3, Z3), U3), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(Y3, Z3), U3), implies(falsehood, falsehood)), Z3), implies(implies(V3, implies(falsehood, W3)), Z3))), true), true, is_a_theorem(implies(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3)), implies(falsehood, implies(Y3, Z3)))), true), true, ifeq(is_a_theorem(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3))), true, is_a_theorem(implies(falsehood, implies(Y3, Z3))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 192.53/28.01  = { by axiom 1 (ifeq_axiom) }
% 192.53/28.01    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(V3, implies(falsehood, W3)), falsehood)), implies(implies(implies(Y3, Z3), U3), falsehood)), Z3), implies(implies(Z3, falsehood), implies(implies(V3, implies(falsehood, W3)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Z3, falsehood), implies(implies(V3, implies(falsehood, W3)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Y3, Z3), U3), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(Y3, Z3), U3), implies(falsehood, falsehood)), Z3), implies(implies(V3, implies(falsehood, W3)), Z3))), true), true, is_a_theorem(implies(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3)), implies(falsehood, implies(Y3, Z3)))), true), true, ifeq(is_a_theorem(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3))), true, is_a_theorem(implies(falsehood, implies(Y3, Z3))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 192.53/28.02  = { by axiom 3 (c0_CAMeredith) }
% 192.53/28.02    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z3, falsehood), implies(implies(V3, implies(falsehood, W3)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Y3, Z3), U3), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(Y3, Z3), U3), implies(falsehood, falsehood)), Z3), implies(implies(V3, implies(falsehood, W3)), Z3))), true), true, is_a_theorem(implies(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3)), implies(falsehood, implies(Y3, Z3)))), true), true, ifeq(is_a_theorem(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3))), true, is_a_theorem(implies(falsehood, implies(Y3, Z3))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 193.45/28.03  = { by axiom 1 (ifeq_axiom) }
% 193.45/28.04    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z3, falsehood), implies(implies(V3, implies(falsehood, W3)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Y3, Z3), U3), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(Y3, Z3), U3), implies(falsehood, falsehood)), Z3), implies(implies(V3, implies(falsehood, W3)), Z3))), true), true, is_a_theorem(implies(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3)), implies(falsehood, implies(Y3, Z3)))), true), true, ifeq(is_a_theorem(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3))), true, is_a_theorem(implies(falsehood, implies(Y3, Z3))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 193.45/28.04  = { by axiom 1 (ifeq_axiom) R->L }
% 193.45/28.04    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Z3, falsehood), implies(implies(V3, implies(falsehood, W3)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Y3, Z3), U3), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(Y3, Z3), U3), implies(falsehood, falsehood)), Z3), implies(implies(V3, implies(falsehood, W3)), Z3))), true), true), true, is_a_theorem(implies(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3)), implies(falsehood, implies(Y3, Z3)))), true), true, ifeq(is_a_theorem(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3))), true, is_a_theorem(implies(falsehood, implies(Y3, Z3))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 193.45/28.05  = { by axiom 3 (c0_CAMeredith) R->L }
% 193.45/28.05    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z3, falsehood), implies(implies(V3, implies(falsehood, W3)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Y3, Z3), U3), implies(falsehood, falsehood))), implies(implies(implies(implies(implies(Y3, Z3), U3), implies(falsehood, falsehood)), Z3), implies(implies(V3, implies(falsehood, W3)), Z3)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z3, falsehood), implies(implies(V3, implies(falsehood, W3)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Y3, Z3), U3), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(Y3, Z3), U3), implies(falsehood, falsehood)), Z3), implies(implies(V3, implies(falsehood, W3)), Z3))), true), true), true, is_a_theorem(implies(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3)), implies(falsehood, implies(Y3, Z3)))), true), true, ifeq(is_a_theorem(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3))), true, is_a_theorem(implies(falsehood, implies(Y3, Z3))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 193.45/28.06  = { by axiom 2 (condensed_detachment) }
% 193.45/28.06    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3)), implies(falsehood, implies(Y3, Z3)))), true), true, ifeq(is_a_theorem(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3))), true, is_a_theorem(implies(falsehood, implies(Y3, Z3))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 193.45/28.07  = { by axiom 1 (ifeq_axiom) }
% 193.45/28.07    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3)), implies(falsehood, implies(Y3, Z3)))), true, ifeq(is_a_theorem(implies(implies(implies(V3, implies(falsehood, W3)), Z3), implies(Y3, Z3))), true, is_a_theorem(implies(falsehood, implies(Y3, Z3))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 193.45/28.08  = { by axiom 2 (condensed_detachment) }
% 193.45/28.08    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 193.45/28.09  = { by axiom 1 (ifeq_axiom) }
% 193.45/28.10    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 193.45/28.11  = { by axiom 1 (ifeq_axiom) R->L }
% 193.45/28.11    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 193.45/28.12  = { by axiom 2 (condensed_detachment) R->L }
% 194.16/28.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), falsehood)), implies(implies(falsehood, implies(Y3, Z3)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), falsehood)), implies(implies(falsehood, implies(Y3, Z3)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.16/28.14  = { by axiom 3 (c0_CAMeredith) }
% 194.16/28.15    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), falsehood)), implies(implies(falsehood, implies(Y3, Z3)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.16/28.16  = { by axiom 1 (ifeq_axiom) }
% 194.16/28.16    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), falsehood)), implies(implies(falsehood, implies(Y3, Z3)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.16/28.18  = { by axiom 3 (c0_CAMeredith) }
% 194.16/28.18    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.64/28.20  = { by axiom 1 (ifeq_axiom) }
% 194.64/28.21    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))))), true, is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.64/28.22  = { by axiom 1 (ifeq_axiom) R->L }
% 194.64/28.22    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))))), true, ifeq(true, true, is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.64/28.24  = { by axiom 2 (condensed_detachment) R->L }
% 194.64/28.25    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), T3), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), T3), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.64/28.27  = { by axiom 3 (c0_CAMeredith) }
% 194.64/28.28    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), T3), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.35/28.31  = { by axiom 1 (ifeq_axiom) }
% 195.35/28.31    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), T3), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.35/28.33  = { by axiom 1 (ifeq_axiom) R->L }
% 195.35/28.34    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), T3), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.35/28.37  = { by axiom 2 (condensed_detachment) R->L }
% 195.35/28.39    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), T3), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), S3), implies(falsehood, falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), S3), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), T3), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), T3), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), S3), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), S3), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), T3), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), T3), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 196.05/28.41  = { by axiom 3 (c0_CAMeredith) }
% 196.05/28.42    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), T3), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), S3), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), S3), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), T3), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), T3), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 196.05/28.44  = { by axiom 1 (ifeq_axiom) }
% 196.05/28.46    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), T3), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), S3), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), S3), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), T3), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), T3), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 196.05/28.48  = { by axiom 1 (ifeq_axiom) R->L }
% 196.05/28.50    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), T3), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), S3), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), S3), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), T3), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), T3), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 196.77/28.52  = { by axiom 3 (c0_CAMeredith) R->L }
% 196.77/28.54    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), T3), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), S3), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), T3), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), T3), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), S3), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), S3), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), T3), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), T3), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 196.77/28.56  = { by axiom 1 (ifeq_axiom) R->L }
% 196.77/28.57    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), T3), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), S3), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), T3), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), T3), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), S3), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), S3), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), T3), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), T3), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 196.77/28.59  = { by axiom 3 (c0_CAMeredith) R->L }
% 197.47/28.61    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), 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% 197.47/28.63  = { by axiom 2 (condensed_detachment) }
% 197.47/28.64    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), 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implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), T3), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), T3), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 197.47/28.66  = { by axiom 1 (ifeq_axiom) }
% 197.47/28.67    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), S3), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), T3), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), T3), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 197.47/28.68  = { by axiom 1 (ifeq_axiom) R->L }
% 197.47/28.70    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), S3), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), T3), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), T3), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 198.16/28.70  = { by axiom 3 (c0_CAMeredith) R->L }
% 198.16/28.72    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), 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implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), S3), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, 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implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), 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implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 198.16/28.72  = { by axiom 2 (condensed_detachment) }
% 198.16/28.73    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 198.16/28.73  = { by axiom 1 (ifeq_axiom) }
% 198.16/28.74    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))))), true, ifeq(is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(falsehood, implies(Y3, Z3)), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 198.16/28.74  = { by axiom 2 (condensed_detachment) }
% 198.16/28.74    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 198.16/28.75  = { by axiom 1 (ifeq_axiom) }
% 198.16/28.75    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 198.16/28.75  = { by axiom 1 (ifeq_axiom) R->L }
% 198.16/28.75    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 198.16/28.76  = { by axiom 3 (c0_CAMeredith) R->L }
% 198.16/28.76    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), X3), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 198.16/28.76  = { by axiom 2 (condensed_detachment) }
% 198.16/28.77    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 198.16/28.77  = { by axiom 1 (ifeq_axiom) }
% 198.16/28.77    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 198.16/28.77  = { by axiom 1 (ifeq_axiom) R->L }
% 198.16/28.78    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 198.16/28.78  = { by axiom 2 (condensed_detachment) R->L }
% 198.16/28.78    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 198.16/28.79  = { by axiom 3 (c0_CAMeredith) }
% 198.16/28.79    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 198.16/28.80  = { by axiom 1 (ifeq_axiom) }
% 198.16/28.80    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 198.16/28.80  = { by axiom 1 (ifeq_axiom) R->L }
% 198.16/28.81    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 198.16/28.82  = { by axiom 2 (condensed_detachment) R->L }
% 198.16/28.82    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 198.16/28.83  = { by axiom 1 (ifeq_axiom) R->L }
% 198.16/28.83    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 199.16/28.84  = { by axiom 2 (condensed_detachment) R->L }
% 199.16/28.84    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Y4, Z4), implies(falsehood, falsehood)), implies(implies(implies(implies(a, b), a), X4), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), implies(implies(implies(implies(a, b), a), X4), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), implies(implies(implies(implies(a, b), a), X4), falsehood)), Y4), implies(falsehood, Y4)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(falsehood, falsehood)), implies(implies(implies(implies(a, b), a), X4), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), implies(implies(implies(implies(a, b), a), X4), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), implies(implies(implies(implies(a, b), a), X4), falsehood)), Y4), implies(falsehood, Y4))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 199.16/28.85  = { by axiom 3 (c0_CAMeredith) }
% 199.16/28.86    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(falsehood, falsehood)), implies(implies(implies(implies(a, b), a), X4), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), implies(implies(implies(implies(a, b), a), X4), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), implies(implies(implies(implies(a, b), a), X4), falsehood)), Y4), implies(falsehood, Y4))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 199.16/28.87  = { by axiom 1 (ifeq_axiom) }
% 199.16/28.87    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(falsehood, falsehood)), implies(implies(implies(implies(a, b), a), X4), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), implies(implies(implies(implies(a, b), a), X4), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), implies(implies(implies(implies(a, b), a), X4), falsehood)), Y4), implies(falsehood, Y4))), true), true, is_a_theorem(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 199.16/28.88  = { by axiom 1 (ifeq_axiom) R->L }
% 199.16/28.89    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(falsehood, falsehood)), implies(implies(implies(implies(a, b), a), X4), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), implies(implies(implies(implies(a, b), a), X4), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), implies(implies(implies(implies(a, b), a), X4), falsehood)), Y4), implies(falsehood, Y4))), true), true, is_a_theorem(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 199.16/28.90  = { by axiom 2 (condensed_detachment) R->L }
% 199.16/28.90    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), falsehood)), implies(implies(Y4, Z4), falsehood)), implies(implies(implies(implies(a, b), a), X4), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), falsehood)), implies(falsehood, falsehood)), implies(implies(Y4, Z4), implies(falsehood, falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), falsehood)), implies(implies(Y4, Z4), falsehood)), implies(implies(implies(implies(a, b), a), X4), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), falsehood)), implies(falsehood, falsehood)), implies(implies(Y4, Z4), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(falsehood, falsehood)), implies(implies(implies(implies(a, b), a), X4), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), implies(implies(implies(implies(a, b), a), X4), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), implies(implies(implies(implies(a, b), a), X4), falsehood)), Y4), implies(falsehood, Y4))), true), true, is_a_theorem(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 199.16/28.91  = { by axiom 3 (c0_CAMeredith) }
% 199.16/28.92    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), falsehood)), implies(implies(Y4, Z4), falsehood)), implies(implies(implies(implies(a, b), a), X4), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), falsehood)), implies(falsehood, falsehood)), implies(implies(Y4, Z4), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(falsehood, falsehood)), implies(implies(implies(implies(a, b), a), X4), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), implies(implies(implies(implies(a, b), a), X4), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), implies(implies(implies(implies(a, b), a), X4), falsehood)), Y4), implies(falsehood, Y4))), true), true, is_a_theorem(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 199.16/28.93  = { by axiom 1 (ifeq_axiom) }
% 199.16/28.93    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), falsehood)), implies(implies(Y4, Z4), falsehood)), implies(implies(implies(implies(a, b), a), X4), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), falsehood)), implies(falsehood, falsehood)), implies(implies(Y4, Z4), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(falsehood, falsehood)), implies(implies(implies(implies(a, b), a), X4), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), implies(implies(implies(implies(a, b), a), X4), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), implies(implies(implies(implies(a, b), a), X4), falsehood)), Y4), implies(falsehood, Y4))), true), true, is_a_theorem(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 199.87/28.94  = { by axiom 3 (c0_CAMeredith) }
% 199.87/28.95    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), falsehood)), implies(falsehood, falsehood)), implies(implies(Y4, Z4), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(falsehood, falsehood)), implies(implies(implies(implies(a, b), a), X4), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), implies(implies(implies(implies(a, b), a), X4), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), implies(implies(implies(implies(a, b), a), X4), falsehood)), Y4), implies(falsehood, Y4))), true), true, is_a_theorem(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 199.87/28.95  = { by axiom 1 (ifeq_axiom) }
% 199.87/28.96    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), falsehood)), implies(falsehood, falsehood)), implies(implies(Y4, Z4), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(falsehood, falsehood)), implies(implies(implies(implies(a, b), a), X4), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), implies(implies(implies(implies(a, b), a), X4), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), implies(implies(implies(implies(a, b), a), X4), falsehood)), Y4), implies(falsehood, Y4))), true), true, is_a_theorem(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 199.87/28.97  = { by axiom 1 (ifeq_axiom) R->L }
% 199.87/28.97    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), falsehood)), implies(falsehood, falsehood)), implies(implies(Y4, Z4), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(falsehood, falsehood)), implies(implies(implies(implies(a, b), a), X4), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), implies(implies(implies(implies(a, b), a), X4), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), implies(implies(implies(implies(a, b), a), X4), falsehood)), Y4), implies(falsehood, Y4))), true), true, is_a_theorem(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 199.87/28.98  = { by axiom 3 (c0_CAMeredith) R->L }
% 199.87/28.99    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), falsehood)), implies(falsehood, falsehood)), implies(implies(Y4, Z4), implies(falsehood, falsehood))), implies(implies(implies(implies(Y4, Z4), implies(falsehood, falsehood)), implies(implies(implies(implies(a, b), a), X4), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), implies(implies(implies(implies(a, b), a), X4), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), falsehood)), implies(falsehood, falsehood)), implies(implies(Y4, Z4), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(falsehood, falsehood)), implies(implies(implies(implies(a, b), a), X4), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), implies(implies(implies(implies(a, b), a), X4), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), implies(implies(implies(implies(a, b), a), X4), falsehood)), Y4), implies(falsehood, Y4))), true), true, is_a_theorem(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 199.87/28.99  = { by axiom 2 (condensed_detachment) }
% 199.87/29.00    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), implies(implies(implies(implies(a, b), a), X4), falsehood)), Y4), implies(falsehood, Y4))), true), true, is_a_theorem(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 199.87/29.01  = { by axiom 1 (ifeq_axiom) }
% 199.87/29.01    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), implies(implies(implies(implies(a, b), a), X4), falsehood)), Y4), implies(falsehood, Y4))), true, is_a_theorem(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 199.87/29.02  = { by axiom 1 (ifeq_axiom) R->L }
% 199.87/29.02    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), implies(implies(implies(implies(a, b), a), X4), falsehood)), Y4), implies(falsehood, Y4))), true, is_a_theorem(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 199.87/29.03  = { by axiom 3 (c0_CAMeredith) R->L }
% 200.54/29.03    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), implies(implies(implies(implies(a, b), a), X4), falsehood)), Y4), implies(falsehood, Y4)), implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), W4), implies(implies(implies(implies(a, b), a), X4), falsehood)), Y4), implies(falsehood, Y4))), true, is_a_theorem(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 200.54/29.04  = { by axiom 2 (condensed_detachment) }
% 200.54/29.04    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 200.54/29.05  = { by axiom 1 (ifeq_axiom) }
% 200.54/29.05    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 200.54/29.06  = { by axiom 1 (ifeq_axiom) R->L }
% 200.54/29.06    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 200.54/29.07  = { by axiom 2 (condensed_detachment) R->L }
% 200.54/29.08    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 200.54/29.09  = { by axiom 3 (c0_CAMeredith) }
% 200.54/29.10    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 200.54/29.11  = { by axiom 1 (ifeq_axiom) }
% 200.54/29.12    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 201.26/29.15  = { by axiom 1 (ifeq_axiom) R->L }
% 201.26/29.16    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 201.26/29.19  = { by axiom 2 (condensed_detachment) R->L }
% 201.73/29.21    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))))), true, ifeq(is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 201.73/29.24  = { by axiom 1 (ifeq_axiom) R->L }
% 201.73/29.25    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 201.73/29.27  = { by axiom 2 (condensed_detachment) R->L }
% 202.43/29.32    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), S4), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), X5), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), X5), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), S4), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), X5), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), X5), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 202.43/29.35  = { by axiom 3 (c0_CAMeredith) }
% 202.43/29.37    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), S4), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), X5), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), X5), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 174.06/29.41  = { by axiom 1 (ifeq_axiom) }
% 174.06/29.43    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), S4), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), X5), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, 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implies(implies(falsehood, Y4), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 174.06/29.46  = { by axiom 1 (ifeq_axiom) R->L }
% 174.06/29.48    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), S4), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), X5), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), X5), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 174.68/29.51  = { by axiom 2 (condensed_detachment) R->L }
% 174.68/29.54    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), 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% 174.68/29.57  = { by axiom 3 (c0_CAMeredith) }
% 174.68/29.59    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, 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implies(implies(falsehood, Y4), falsehood)), falsehood), S4), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), S4), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, 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implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, 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implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), 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% 175.29/29.62  = { by axiom 1 (ifeq_axiom) }
% 175.29/29.64    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, 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implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), X5), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), S4), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), S4), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), X5), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), X5), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 175.29/29.67  = { by axiom 3 (c0_CAMeredith) }
% 175.29/29.69    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, 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falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), 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falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), X5), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), 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implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, 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implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 175.88/29.72  = { by axiom 1 (ifeq_axiom) }
% 175.88/29.74    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, 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falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), 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implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 175.88/29.76  = { by axiom 1 (ifeq_axiom) R->L }
% 175.88/29.78    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), X5), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), S4), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), S4), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), X5), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), X5), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 176.49/29.81  = { by axiom 3 (c0_CAMeredith) R->L }
% 176.49/29.83    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), 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falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, 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true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 176.49/29.85  = { by axiom 2 (condensed_detachment) }
% 176.49/29.87    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, 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falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), X5), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 176.49/29.89  = { by axiom 1 (ifeq_axiom) }
% 177.09/29.91    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), X5), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 177.09/29.92  = { by axiom 1 (ifeq_axiom) R->L }
% 177.09/29.94    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), X5), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 177.09/29.95  = { by axiom 3 (c0_CAMeredith) R->L }
% 177.09/29.97    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), X5), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), X5), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 177.09/29.98  = { by axiom 2 (condensed_detachment) }
% 177.09/29.99    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))))), true, ifeq(true, true, is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 177.09/30.00  = { by axiom 1 (ifeq_axiom) }
% 177.09/30.01    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))))), true, is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 177.89/30.03  = { by axiom 1 (ifeq_axiom) R->L }
% 177.89/30.04    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))))), true), true, is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 177.89/30.06  = { by axiom 3 (c0_CAMeredith) R->L }
% 177.89/30.08    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), falsehood)), implies(implies(falsehood, implies(U4, T4)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))))), true), true, is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 177.89/30.08  = { by axiom 1 (ifeq_axiom) R->L }
% 177.89/30.10    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), falsehood)), implies(implies(falsehood, implies(U4, T4)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 177.89/30.10  = { by axiom 3 (c0_CAMeredith) R->L }
% 177.89/30.12    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), falsehood)), implies(implies(falsehood, implies(U4, T4)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), falsehood)), implies(implies(falsehood, implies(U4, T4)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 178.50/30.13  = { by axiom 2 (condensed_detachment) }
% 178.50/30.14    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 178.50/30.15  = { by axiom 1 (ifeq_axiom) }
% 178.50/30.16    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 178.50/30.17  = { by axiom 1 (ifeq_axiom) R->L }
% 178.50/30.17    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 178.50/30.18  = { by axiom 2 (condensed_detachment) R->L }
% 178.50/30.19    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4)), implies(falsehood, implies(U4, T4)))), true, ifeq(is_a_theorem(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4))), true, is_a_theorem(implies(falsehood, implies(U4, T4))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 178.91/30.20  = { by axiom 1 (ifeq_axiom) R->L }
% 178.91/30.21    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4)), implies(falsehood, implies(U4, T4)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4))), true, is_a_theorem(implies(falsehood, implies(U4, T4))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 178.91/30.22  = { by axiom 2 (condensed_detachment) R->L }
% 178.91/30.23    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T4, falsehood), implies(implies(Y5, implies(falsehood, Z5)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(U4, T4), W5), implies(falsehood, falsehood))), implies(implies(implies(implies(implies(U4, T4), W5), implies(falsehood, falsehood)), T4), implies(implies(Y5, implies(falsehood, Z5)), T4)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(T4, falsehood), implies(implies(Y5, implies(falsehood, Z5)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(U4, T4), W5), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(U4, T4), W5), implies(falsehood, falsehood)), T4), implies(implies(Y5, implies(falsehood, Z5)), T4))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4)), implies(falsehood, implies(U4, T4)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4))), true, is_a_theorem(implies(falsehood, implies(U4, T4))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 178.91/30.24  = { by axiom 3 (c0_CAMeredith) }
% 178.91/30.24    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(T4, falsehood), implies(implies(Y5, implies(falsehood, Z5)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(U4, T4), W5), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(U4, T4), W5), implies(falsehood, falsehood)), T4), implies(implies(Y5, implies(falsehood, Z5)), T4))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4)), implies(falsehood, implies(U4, T4)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4))), true, is_a_theorem(implies(falsehood, implies(U4, T4))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 178.91/30.25  = { by axiom 1 (ifeq_axiom) }
% 178.91/30.26    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T4, falsehood), implies(implies(Y5, implies(falsehood, Z5)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(U4, T4), W5), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(U4, T4), W5), implies(falsehood, falsehood)), T4), implies(implies(Y5, implies(falsehood, Z5)), T4))), true), true, is_a_theorem(implies(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4)), implies(falsehood, implies(U4, T4)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4))), true, is_a_theorem(implies(falsehood, implies(U4, T4))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 178.91/30.27  = { by axiom 1 (ifeq_axiom) R->L }
% 178.91/30.28    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T4, falsehood), implies(implies(Y5, implies(falsehood, Z5)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(U4, T4), W5), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(U4, T4), W5), implies(falsehood, falsehood)), T4), implies(implies(Y5, implies(falsehood, Z5)), T4))), true), true, is_a_theorem(implies(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4)), implies(falsehood, implies(U4, T4)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4))), true, is_a_theorem(implies(falsehood, implies(U4, T4))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 178.91/30.29  = { by axiom 3 (c0_CAMeredith) R->L }
% 179.51/30.30    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(Y5, implies(falsehood, Z5)), falsehood)), implies(implies(implies(U4, T4), W5), falsehood)), T4), implies(implies(T4, falsehood), implies(implies(Y5, implies(falsehood, Z5)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(T4, falsehood), implies(implies(Y5, implies(falsehood, Z5)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(U4, T4), W5), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(U4, T4), W5), implies(falsehood, falsehood)), T4), implies(implies(Y5, implies(falsehood, Z5)), T4))), true), true, is_a_theorem(implies(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4)), implies(falsehood, implies(U4, T4)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4))), true, is_a_theorem(implies(falsehood, implies(U4, T4))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 179.51/30.31  = { by axiom 1 (ifeq_axiom) R->L }
% 179.51/30.32    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(Y5, implies(falsehood, Z5)), falsehood)), implies(implies(implies(U4, T4), W5), falsehood)), T4), implies(implies(T4, falsehood), implies(implies(Y5, implies(falsehood, Z5)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(T4, falsehood), implies(implies(Y5, implies(falsehood, Z5)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(U4, T4), W5), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(U4, T4), W5), implies(falsehood, falsehood)), T4), implies(implies(Y5, implies(falsehood, Z5)), T4))), true), true, is_a_theorem(implies(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4)), implies(falsehood, implies(U4, T4)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4))), true, is_a_theorem(implies(falsehood, implies(U4, T4))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 179.51/30.33  = { by axiom 3 (c0_CAMeredith) R->L }
% 179.51/30.33    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(Y5, implies(falsehood, Z5)), falsehood)), implies(implies(implies(U4, T4), W5), falsehood)), T4), implies(implies(T4, falsehood), implies(implies(Y5, implies(falsehood, Z5)), falsehood))), implies(implies(implies(implies(T4, falsehood), implies(implies(Y5, implies(falsehood, Z5)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(U4, T4), W5), implies(falsehood, falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(Y5, implies(falsehood, Z5)), falsehood)), implies(implies(implies(U4, T4), W5), falsehood)), T4), implies(implies(T4, falsehood), implies(implies(Y5, implies(falsehood, Z5)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(T4, falsehood), implies(implies(Y5, implies(falsehood, Z5)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(U4, T4), W5), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(U4, T4), W5), implies(falsehood, falsehood)), T4), implies(implies(Y5, implies(falsehood, Z5)), T4))), true), true, is_a_theorem(implies(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4)), implies(falsehood, implies(U4, T4)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4))), true, is_a_theorem(implies(falsehood, implies(U4, T4))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 179.51/30.34  = { by axiom 2 (condensed_detachment) }
% 179.51/30.35    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(U4, T4), W5), implies(falsehood, falsehood)), T4), implies(implies(Y5, implies(falsehood, Z5)), T4))), true), true, is_a_theorem(implies(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4)), implies(falsehood, implies(U4, T4)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4))), true, is_a_theorem(implies(falsehood, implies(U4, T4))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 179.51/30.36  = { by axiom 1 (ifeq_axiom) }
% 179.51/30.37    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(U4, T4), W5), implies(falsehood, falsehood)), T4), implies(implies(Y5, implies(falsehood, Z5)), T4))), true, is_a_theorem(implies(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4)), implies(falsehood, implies(U4, T4)))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4))), true, is_a_theorem(implies(falsehood, implies(U4, T4))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 179.51/30.38  = { by axiom 1 (ifeq_axiom) R->L }
% 179.51/30.38    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(U4, T4), W5), implies(falsehood, falsehood)), T4), implies(implies(Y5, implies(falsehood, Z5)), T4))), true, is_a_theorem(implies(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4)), implies(falsehood, implies(U4, T4)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4))), true, is_a_theorem(implies(falsehood, implies(U4, T4))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 179.51/30.39  = { by axiom 3 (c0_CAMeredith) R->L }
% 180.11/30.40    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(U4, T4), W5), implies(falsehood, falsehood)), T4), implies(implies(Y5, implies(falsehood, Z5)), T4)), implies(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4)), implies(falsehood, implies(U4, T4))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(U4, T4), W5), implies(falsehood, falsehood)), T4), implies(implies(Y5, implies(falsehood, Z5)), T4))), true, is_a_theorem(implies(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4)), implies(falsehood, implies(U4, T4)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4))), true, is_a_theorem(implies(falsehood, implies(U4, T4))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 180.11/30.41  = { by axiom 2 (condensed_detachment) }
% 180.11/30.41    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4))), true, is_a_theorem(implies(falsehood, implies(U4, T4))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 180.11/30.42  = { by axiom 1 (ifeq_axiom) }
% 180.11/30.43    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4))), true, is_a_theorem(implies(falsehood, implies(U4, T4))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 180.11/30.44  = { by axiom 1 (ifeq_axiom) R->L }
% 180.11/30.45    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4))), true), true, is_a_theorem(implies(falsehood, implies(U4, T4))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 180.11/30.46  = { by axiom 2 (condensed_detachment) R->L }
% 180.11/30.46    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, Z5), implies(U4, falsehood)), implies(Y5, falsehood)), T4), implies(implies(T4, falsehood), implies(U4, falsehood))), implies(implies(implies(implies(T4, falsehood), implies(U4, falsehood)), implies(falsehood, Z5)), implies(Y5, implies(falsehood, Z5))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, Z5), implies(U4, falsehood)), implies(Y5, falsehood)), T4), implies(implies(T4, falsehood), implies(U4, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(T4, falsehood), implies(U4, falsehood)), implies(falsehood, Z5)), implies(Y5, implies(falsehood, Z5)))), true), true), true, is_a_theorem(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4))), true), true, is_a_theorem(implies(falsehood, implies(U4, T4))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 180.11/30.47  = { by axiom 3 (c0_CAMeredith) }
% 180.11/30.48    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, Z5), implies(U4, falsehood)), implies(Y5, falsehood)), T4), implies(implies(T4, falsehood), implies(U4, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(T4, falsehood), implies(U4, falsehood)), implies(falsehood, Z5)), implies(Y5, implies(falsehood, Z5)))), true), true), true, is_a_theorem(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4))), true), true, is_a_theorem(implies(falsehood, implies(U4, T4))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 180.11/30.49  = { by axiom 1 (ifeq_axiom) }
% 180.11/30.50    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, Z5), implies(U4, falsehood)), implies(Y5, falsehood)), T4), implies(implies(T4, falsehood), implies(U4, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(T4, falsehood), implies(U4, falsehood)), implies(falsehood, Z5)), implies(Y5, implies(falsehood, Z5)))), true), true, is_a_theorem(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4))), true), true, is_a_theorem(implies(falsehood, implies(U4, T4))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 180.72/30.51  = { by axiom 3 (c0_CAMeredith) }
% 180.72/30.51    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T4, falsehood), implies(U4, falsehood)), implies(falsehood, Z5)), implies(Y5, implies(falsehood, Z5)))), true), true, is_a_theorem(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4))), true), true, is_a_theorem(implies(falsehood, implies(U4, T4))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 180.72/30.52  = { by axiom 1 (ifeq_axiom) }
% 180.72/30.53    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T4, falsehood), implies(U4, falsehood)), implies(falsehood, Z5)), implies(Y5, implies(falsehood, Z5)))), true, is_a_theorem(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4))), true), true, is_a_theorem(implies(falsehood, implies(U4, T4))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 180.72/30.54  = { by axiom 1 (ifeq_axiom) R->L }
% 180.72/30.54    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(T4, falsehood), implies(U4, falsehood)), implies(falsehood, Z5)), implies(Y5, implies(falsehood, Z5)))), true, is_a_theorem(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4))), true), true), true, is_a_theorem(implies(falsehood, implies(U4, T4))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 180.72/30.55  = { by axiom 3 (c0_CAMeredith) R->L }
% 180.72/30.56    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T4, falsehood), implies(U4, falsehood)), implies(falsehood, Z5)), implies(Y5, implies(falsehood, Z5))), implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(T4, falsehood), implies(U4, falsehood)), implies(falsehood, Z5)), implies(Y5, implies(falsehood, Z5)))), true, is_a_theorem(implies(implies(implies(Y5, implies(falsehood, Z5)), T4), implies(U4, T4))), true), true), true, is_a_theorem(implies(falsehood, implies(U4, T4))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 180.72/30.57  = { by axiom 2 (condensed_detachment) }
% 180.72/30.57    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(falsehood, implies(U4, T4))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 180.72/30.58  = { by axiom 1 (ifeq_axiom) }
% 180.72/30.58    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U4, T4)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood))))), true, ifeq(is_a_theorem(implies(falsehood, implies(U4, T4))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 180.72/30.59  = { by axiom 2 (condensed_detachment) }
% 180.72/30.59    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 181.33/30.60  = { by axiom 1 (ifeq_axiom) }
% 181.33/30.61    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 181.33/30.61  = { by axiom 1 (ifeq_axiom) R->L }
% 181.33/30.61    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 181.33/30.62  = { by axiom 3 (c0_CAMeredith) R->L }
% 181.33/30.62    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), V4), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 181.33/30.63  = { by axiom 2 (condensed_detachment) }
% 181.33/30.63    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 181.33/30.63  = { by axiom 1 (ifeq_axiom) }
% 181.33/30.64    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 181.33/30.64  = { by axiom 1 (ifeq_axiom) R->L }
% 181.33/30.64    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 181.33/30.64  = { by axiom 3 (c0_CAMeredith) R->L }
% 181.33/30.66    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(falsehood, S2), falsehood)), implies(implies(falsehood, Y4), falsehood)), implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), X4), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 181.33/30.66  = { by axiom 2 (condensed_detachment) }
% 181.33/30.67    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 181.33/30.67  = { by axiom 1 (ifeq_axiom) }
% 181.33/30.67    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(a, b), a)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 181.33/30.67  = { by axiom 2 (condensed_detachment) }
% 181.33/30.67    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 181.33/30.67  = { by axiom 1 (ifeq_axiom) }
% 181.33/30.67    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 181.33/30.67  = { by axiom 1 (ifeq_axiom) R->L }
% 181.33/30.67    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 181.33/30.68  = { by axiom 2 (condensed_detachment) R->L }
% 181.33/30.68    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 181.33/30.68  = { by axiom 1 (ifeq_axiom) R->L }
% 181.33/30.68    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 181.33/30.69  = { by axiom 2 (condensed_detachment) R->L }
% 181.33/30.69    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 181.33/30.69  = { by axiom 3 (c0_CAMeredith) }
% 181.33/30.70    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 181.95/30.70  = { by axiom 1 (ifeq_axiom) }
% 181.95/30.70    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 181.95/30.71  = { by axiom 1 (ifeq_axiom) R->L }
% 181.95/30.72    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 181.95/30.72  = { by axiom 2 (condensed_detachment) R->L }
% 181.95/30.73    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 181.95/30.74  = { by axiom 1 (ifeq_axiom) R->L }
% 181.95/30.74    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 181.95/30.75  = { by axiom 2 (condensed_detachment) R->L }
% 181.95/30.75    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T5, S5), implies(falsehood, falsehood)), implies(implies(falsehood, V5), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), implies(implies(falsehood, V5), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), implies(implies(falsehood, V5), falsehood)), T5), implies(falsehood, T5)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(T5, S5), implies(falsehood, falsehood)), implies(implies(falsehood, V5), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), implies(implies(falsehood, V5), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), implies(implies(falsehood, V5), falsehood)), T5), implies(falsehood, T5))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 181.95/30.76  = { by axiom 3 (c0_CAMeredith) }
% 181.95/30.77    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(T5, S5), implies(falsehood, falsehood)), implies(implies(falsehood, V5), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), implies(implies(falsehood, V5), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), implies(implies(falsehood, V5), falsehood)), T5), implies(falsehood, T5))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 181.95/30.78  = { by axiom 1 (ifeq_axiom) }
% 181.95/30.78    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T5, S5), implies(falsehood, falsehood)), implies(implies(falsehood, V5), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), implies(implies(falsehood, V5), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), implies(implies(falsehood, V5), falsehood)), T5), implies(falsehood, T5))), true), true, is_a_theorem(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 181.95/30.79  = { by axiom 1 (ifeq_axiom) R->L }
% 181.95/30.80    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T5, S5), implies(falsehood, falsehood)), implies(implies(falsehood, V5), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), implies(implies(falsehood, V5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), implies(implies(falsehood, V5), falsehood)), T5), implies(falsehood, T5))), true), true, is_a_theorem(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 182.53/30.81  = { by axiom 2 (condensed_detachment) R->L }
% 182.53/30.81    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), falsehood)), implies(implies(T5, S5), falsehood)), implies(implies(falsehood, V5), falsehood)), implies(implies(implies(implies(falsehood, V5), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), falsehood))), implies(implies(implies(implies(implies(implies(falsehood, V5), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), falsehood)), implies(falsehood, falsehood)), implies(implies(T5, S5), implies(falsehood, falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), falsehood)), implies(implies(T5, S5), falsehood)), implies(implies(falsehood, V5), falsehood)), implies(implies(implies(implies(falsehood, V5), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), falsehood)), implies(falsehood, falsehood)), implies(implies(T5, S5), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(T5, S5), implies(falsehood, falsehood)), implies(implies(falsehood, V5), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), implies(implies(falsehood, V5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), implies(implies(falsehood, V5), falsehood)), T5), implies(falsehood, T5))), true), true, is_a_theorem(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 182.53/30.82  = { by axiom 3 (c0_CAMeredith) }
% 182.53/30.83    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), falsehood)), implies(implies(T5, S5), falsehood)), implies(implies(falsehood, V5), falsehood)), implies(implies(implies(implies(falsehood, V5), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), falsehood)), implies(falsehood, falsehood)), implies(implies(T5, S5), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(T5, S5), implies(falsehood, falsehood)), implies(implies(falsehood, V5), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), implies(implies(falsehood, V5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), implies(implies(falsehood, V5), falsehood)), T5), implies(falsehood, T5))), true), true, is_a_theorem(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 182.53/30.84  = { by axiom 1 (ifeq_axiom) }
% 182.53/30.84    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), falsehood)), implies(implies(T5, S5), falsehood)), implies(implies(falsehood, V5), falsehood)), implies(implies(implies(implies(falsehood, V5), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), falsehood)), implies(falsehood, falsehood)), implies(implies(T5, S5), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(T5, S5), implies(falsehood, falsehood)), implies(implies(falsehood, V5), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), implies(implies(falsehood, V5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), implies(implies(falsehood, V5), falsehood)), T5), implies(falsehood, T5))), true), true, is_a_theorem(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 182.53/30.85  = { by axiom 3 (c0_CAMeredith) }
% 182.53/30.86    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), falsehood)), implies(falsehood, falsehood)), implies(implies(T5, S5), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(T5, S5), implies(falsehood, falsehood)), implies(implies(falsehood, V5), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), implies(implies(falsehood, V5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), implies(implies(falsehood, V5), falsehood)), T5), implies(falsehood, T5))), true), true, is_a_theorem(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 182.53/30.86  = { by axiom 1 (ifeq_axiom) }
% 182.53/30.87    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), falsehood)), implies(falsehood, falsehood)), implies(implies(T5, S5), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(T5, S5), implies(falsehood, falsehood)), implies(implies(falsehood, V5), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), implies(implies(falsehood, V5), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), implies(implies(falsehood, V5), falsehood)), T5), implies(falsehood, T5))), true), true, is_a_theorem(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 182.53/30.88  = { by axiom 1 (ifeq_axiom) R->L }
% 182.53/30.88    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), falsehood)), implies(falsehood, falsehood)), implies(implies(T5, S5), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(T5, S5), implies(falsehood, falsehood)), implies(implies(falsehood, V5), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), implies(implies(falsehood, V5), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), implies(implies(falsehood, V5), falsehood)), T5), implies(falsehood, T5))), true), true, is_a_theorem(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 182.53/30.89  = { by axiom 3 (c0_CAMeredith) R->L }
% 183.14/30.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, V5), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), falsehood)), implies(falsehood, falsehood)), implies(implies(T5, S5), implies(falsehood, falsehood))), implies(implies(implies(implies(T5, S5), implies(falsehood, falsehood)), implies(implies(falsehood, V5), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), implies(implies(falsehood, V5), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), falsehood)), implies(falsehood, falsehood)), implies(implies(T5, S5), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(T5, S5), implies(falsehood, falsehood)), implies(implies(falsehood, V5), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), implies(implies(falsehood, V5), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), implies(implies(falsehood, V5), falsehood)), T5), implies(falsehood, T5))), true), true, is_a_theorem(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 183.14/30.91  = { by axiom 2 (condensed_detachment) }
% 183.14/30.91    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), implies(implies(falsehood, V5), falsehood)), T5), implies(falsehood, T5))), true), true, is_a_theorem(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 183.14/30.92  = { by axiom 1 (ifeq_axiom) }
% 183.14/30.92    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), implies(implies(falsehood, V5), falsehood)), T5), implies(falsehood, T5))), true, is_a_theorem(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 183.14/30.93  = { by axiom 1 (ifeq_axiom) R->L }
% 183.14/30.93    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), implies(implies(falsehood, V5), falsehood)), T5), implies(falsehood, T5))), true, is_a_theorem(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 183.14/30.94  = { by axiom 3 (c0_CAMeredith) R->L }
% 183.14/30.94    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), implies(implies(falsehood, V5), falsehood)), T5), implies(falsehood, T5)), implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), X6), implies(implies(falsehood, V5), falsehood)), T5), implies(falsehood, T5))), true, is_a_theorem(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 183.14/30.95  = { by axiom 2 (condensed_detachment) }
% 183.14/30.96    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 183.14/30.97  = { by axiom 1 (ifeq_axiom) }
% 183.14/30.97    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 183.14/30.98  = { by axiom 1 (ifeq_axiom) R->L }
% 183.14/30.98    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 183.14/30.99  = { by axiom 2 (condensed_detachment) R->L }
% 183.14/31.00    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 183.14/31.01  = { by axiom 3 (c0_CAMeredith) }
% 183.14/31.02    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 184.05/31.06  = { by axiom 1 (ifeq_axiom) }
% 184.05/31.07    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 184.05/31.14  = { by axiom 1 (ifeq_axiom) R->L }
% 184.05/31.15    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 184.95/31.24  = { by axiom 2 (condensed_detachment) R->L }
% 184.95/31.28    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))))), true, ifeq(is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 185.56/31.35  = { by axiom 1 (ifeq_axiom) R->L }
% 185.56/31.39    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), 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implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 186.16/31.46  = { by axiom 2 (condensed_detachment) R->L }
% 186.16/31.50    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), 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falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), U6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), 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implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), V6), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, 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falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), U6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), 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implies(implies(falsehood, T5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), 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Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), 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implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), 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falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 186.78/31.55  = { by axiom 3 (c0_CAMeredith) }
% 186.78/31.57    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), 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falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), 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falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 187.37/31.66  = { by axiom 1 (ifeq_axiom) }
% 187.37/31.69    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), V6), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, 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falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), U6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), 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implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 187.97/31.74  = { by axiom 1 (ifeq_axiom) R->L }
% 187.97/31.75    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), 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falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), U6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), 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implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), 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true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), 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implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), 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implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, 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% 187.97/31.78  = { by axiom 2 (condensed_detachment) R->L }
% 188.59/31.80    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), 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falsehood), falsehood), implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), U6), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), 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% 188.59/31.83  = { by axiom 3 (c0_CAMeredith) }
% 188.59/31.86    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), 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implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), 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implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, 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% 188.59/31.88  = { by axiom 1 (ifeq_axiom) }
% 189.19/31.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), 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% 189.19/31.93  = { by axiom 3 (c0_CAMeredith) }
% 189.19/31.95    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), U6), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), V6), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), V6), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), U6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), U6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 189.19/31.98  = { by axiom 1 (ifeq_axiom) }
% 189.19/31.99    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), 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T5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), 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U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, 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implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, 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% 189.19/32.01  = { by axiom 1 (ifeq_axiom) R->L }
% 189.19/32.03    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), 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implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), 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is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), 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% 189.99/32.05  = { by axiom 3 (c0_CAMeredith) R->L }
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falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 189.99/32.09  = { by axiom 2 (condensed_detachment) }
% 189.99/32.10    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), U6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 189.99/32.12  = { by axiom 1 (ifeq_axiom) }
% 190.60/32.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), U6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 190.60/32.15  = { by axiom 1 (ifeq_axiom) R->L }
% 190.60/32.16    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), U6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 190.60/32.16  = { by axiom 3 (c0_CAMeredith) R->L }
% 190.60/32.18    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), U6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))), implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), 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implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), U6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), 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% 190.60/32.19  = { by axiom 2 (condensed_detachment) }
% 190.60/32.19    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), 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implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.00/32.20  = { by axiom 1 (ifeq_axiom) }
% 191.00/32.21    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))))), true, is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.00/32.23  = { by axiom 1 (ifeq_axiom) R->L }
% 191.00/32.23    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), 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implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), 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implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, 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% 191.00/32.25  = { by axiom 3 (c0_CAMeredith) R->L }
% 191.00/32.26    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), 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falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), 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is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), 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implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), 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falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.00/32.26  = { by axiom 1 (ifeq_axiom) R->L }
% 191.00/32.27    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), falsehood)), implies(implies(falsehood, implies(Z6, W6)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.00/32.28  = { by axiom 3 (c0_CAMeredith) R->L }
% 191.00/32.29    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), falsehood)), implies(implies(falsehood, implies(Z6, W6)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), 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% 191.00/32.30  = { by axiom 2 (condensed_detachment) }
% 191.60/32.30    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, 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falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.60/32.31  = { by axiom 1 (ifeq_axiom) }
% 191.60/32.31    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.60/32.32  = { by axiom 1 (ifeq_axiom) R->L }
% 191.60/32.32    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.60/32.33  = { by axiom 2 (condensed_detachment) R->L }
% 191.60/32.34    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6)), implies(falsehood, implies(Z6, W6)))), true, ifeq(is_a_theorem(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6))), true, is_a_theorem(implies(falsehood, implies(Z6, W6))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.60/32.34  = { by axiom 1 (ifeq_axiom) R->L }
% 191.60/32.35    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6)), implies(falsehood, implies(Z6, W6)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6))), true, is_a_theorem(implies(falsehood, implies(Z6, W6))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.60/32.35  = { by axiom 2 (condensed_detachment) R->L }
% 191.60/32.36    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(W6, falsehood), implies(implies(T6, implies(falsehood, S6)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Z6, W6), X7), implies(falsehood, falsehood))), implies(implies(implies(implies(implies(Z6, W6), X7), implies(falsehood, falsehood)), W6), implies(implies(T6, implies(falsehood, S6)), W6)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(W6, falsehood), implies(implies(T6, implies(falsehood, S6)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Z6, W6), X7), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(Z6, W6), X7), implies(falsehood, falsehood)), W6), implies(implies(T6, implies(falsehood, S6)), W6))), true), true), true, is_a_theorem(implies(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6)), implies(falsehood, implies(Z6, W6)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6))), true, is_a_theorem(implies(falsehood, implies(Z6, W6))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.60/32.37  = { by axiom 3 (c0_CAMeredith) }
% 191.60/32.37    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(W6, falsehood), implies(implies(T6, implies(falsehood, S6)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Z6, W6), X7), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(Z6, W6), X7), implies(falsehood, falsehood)), W6), implies(implies(T6, implies(falsehood, S6)), W6))), true), true), true, is_a_theorem(implies(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6)), implies(falsehood, implies(Z6, W6)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6))), true, is_a_theorem(implies(falsehood, implies(Z6, W6))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.60/32.38  = { by axiom 1 (ifeq_axiom) }
% 191.60/32.38    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W6, falsehood), implies(implies(T6, implies(falsehood, S6)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Z6, W6), X7), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(Z6, W6), X7), implies(falsehood, falsehood)), W6), implies(implies(T6, implies(falsehood, S6)), W6))), true), true, is_a_theorem(implies(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6)), implies(falsehood, implies(Z6, W6)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6))), true, is_a_theorem(implies(falsehood, implies(Z6, W6))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 191.60/32.39  = { by axiom 1 (ifeq_axiom) R->L }
% 191.60/32.40    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W6, falsehood), implies(implies(T6, implies(falsehood, S6)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Z6, W6), X7), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(Z6, W6), X7), implies(falsehood, falsehood)), W6), implies(implies(T6, implies(falsehood, S6)), W6))), true), true, is_a_theorem(implies(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6)), implies(falsehood, implies(Z6, W6)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6))), true, is_a_theorem(implies(falsehood, implies(Z6, W6))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 192.21/32.40  = { by axiom 3 (c0_CAMeredith) R->L }
% 192.21/32.41    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(T6, implies(falsehood, S6)), falsehood)), implies(implies(implies(Z6, W6), X7), falsehood)), W6), implies(implies(W6, falsehood), implies(implies(T6, implies(falsehood, S6)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(W6, falsehood), implies(implies(T6, implies(falsehood, S6)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Z6, W6), X7), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(Z6, W6), X7), implies(falsehood, falsehood)), W6), implies(implies(T6, implies(falsehood, S6)), W6))), true), true, is_a_theorem(implies(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6)), implies(falsehood, implies(Z6, W6)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6))), true, is_a_theorem(implies(falsehood, implies(Z6, W6))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 192.21/32.43  = { by axiom 1 (ifeq_axiom) R->L }
% 192.21/32.43    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(T6, implies(falsehood, S6)), falsehood)), implies(implies(implies(Z6, W6), X7), falsehood)), W6), implies(implies(W6, falsehood), implies(implies(T6, implies(falsehood, S6)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(W6, falsehood), implies(implies(T6, implies(falsehood, S6)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Z6, W6), X7), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(Z6, W6), X7), implies(falsehood, falsehood)), W6), implies(implies(T6, implies(falsehood, S6)), W6))), true), true, is_a_theorem(implies(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6)), implies(falsehood, implies(Z6, W6)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6))), true, is_a_theorem(implies(falsehood, implies(Z6, W6))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 192.21/32.44  = { by axiom 3 (c0_CAMeredith) R->L }
% 192.21/32.44    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(T6, implies(falsehood, S6)), falsehood)), implies(implies(implies(Z6, W6), X7), falsehood)), W6), implies(implies(W6, falsehood), implies(implies(T6, implies(falsehood, S6)), falsehood))), implies(implies(implies(implies(W6, falsehood), implies(implies(T6, implies(falsehood, S6)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Z6, W6), X7), implies(falsehood, falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(T6, implies(falsehood, S6)), falsehood)), implies(implies(implies(Z6, W6), X7), falsehood)), W6), implies(implies(W6, falsehood), implies(implies(T6, implies(falsehood, S6)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(W6, falsehood), implies(implies(T6, implies(falsehood, S6)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Z6, W6), X7), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(Z6, W6), X7), implies(falsehood, falsehood)), W6), implies(implies(T6, implies(falsehood, S6)), W6))), true), true, is_a_theorem(implies(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6)), implies(falsehood, implies(Z6, W6)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6))), true, is_a_theorem(implies(falsehood, implies(Z6, W6))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 192.21/32.45  = { by axiom 2 (condensed_detachment) }
% 192.21/32.46    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(Z6, W6), X7), implies(falsehood, falsehood)), W6), implies(implies(T6, implies(falsehood, S6)), W6))), true), true, is_a_theorem(implies(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6)), implies(falsehood, implies(Z6, W6)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6))), true, is_a_theorem(implies(falsehood, implies(Z6, W6))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 192.21/32.46  = { by axiom 1 (ifeq_axiom) }
% 192.21/32.47    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z6, W6), X7), implies(falsehood, falsehood)), W6), implies(implies(T6, implies(falsehood, S6)), W6))), true, is_a_theorem(implies(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6)), implies(falsehood, implies(Z6, W6)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6))), true, is_a_theorem(implies(falsehood, implies(Z6, W6))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 192.21/32.47  = { by axiom 1 (ifeq_axiom) R->L }
% 192.21/32.48    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z6, W6), X7), implies(falsehood, falsehood)), W6), implies(implies(T6, implies(falsehood, S6)), W6))), true, is_a_theorem(implies(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6)), implies(falsehood, implies(Z6, W6)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6))), true, is_a_theorem(implies(falsehood, implies(Z6, W6))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 192.21/32.49  = { by axiom 3 (c0_CAMeredith) R->L }
% 192.21/32.49    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(Z6, W6), X7), implies(falsehood, falsehood)), W6), implies(implies(T6, implies(falsehood, S6)), W6)), implies(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6)), implies(falsehood, implies(Z6, W6))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z6, W6), X7), implies(falsehood, falsehood)), W6), implies(implies(T6, implies(falsehood, S6)), W6))), true, is_a_theorem(implies(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6)), implies(falsehood, implies(Z6, W6)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6))), true, is_a_theorem(implies(falsehood, implies(Z6, W6))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 192.21/32.50  = { by axiom 2 (condensed_detachment) }
% 192.82/32.50    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6))), true, is_a_theorem(implies(falsehood, implies(Z6, W6))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 192.82/32.51  = { by axiom 1 (ifeq_axiom) }
% 192.82/32.51    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6))), true, is_a_theorem(implies(falsehood, implies(Z6, W6))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 192.82/32.52  = { by axiom 1 (ifeq_axiom) R->L }
% 192.82/32.52    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6))), true), true, is_a_theorem(implies(falsehood, implies(Z6, W6))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 192.82/32.53  = { by axiom 2 (condensed_detachment) R->L }
% 192.82/32.54    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, S6), implies(Z6, falsehood)), implies(T6, falsehood)), W6), implies(implies(W6, falsehood), implies(Z6, falsehood))), implies(implies(implies(implies(W6, falsehood), implies(Z6, falsehood)), implies(falsehood, S6)), implies(T6, implies(falsehood, S6))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S6), implies(Z6, falsehood)), implies(T6, falsehood)), W6), implies(implies(W6, falsehood), implies(Z6, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(W6, falsehood), implies(Z6, falsehood)), implies(falsehood, S6)), implies(T6, implies(falsehood, S6)))), true), true), true, is_a_theorem(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6))), true), true, is_a_theorem(implies(falsehood, implies(Z6, W6))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 192.82/32.54  = { by axiom 3 (c0_CAMeredith) }
% 192.82/32.55    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S6), implies(Z6, falsehood)), implies(T6, falsehood)), W6), implies(implies(W6, falsehood), implies(Z6, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(W6, falsehood), implies(Z6, falsehood)), implies(falsehood, S6)), implies(T6, implies(falsehood, S6)))), true), true), true, is_a_theorem(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6))), true), true, is_a_theorem(implies(falsehood, implies(Z6, W6))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 192.82/32.55  = { by axiom 1 (ifeq_axiom) }
% 192.82/32.56    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S6), implies(Z6, falsehood)), implies(T6, falsehood)), W6), implies(implies(W6, falsehood), implies(Z6, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(W6, falsehood), implies(Z6, falsehood)), implies(falsehood, S6)), implies(T6, implies(falsehood, S6)))), true), true, is_a_theorem(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6))), true), true, is_a_theorem(implies(falsehood, implies(Z6, W6))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 192.82/32.56  = { by axiom 3 (c0_CAMeredith) }
% 192.82/32.57    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W6, falsehood), implies(Z6, falsehood)), implies(falsehood, S6)), implies(T6, implies(falsehood, S6)))), true), true, is_a_theorem(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6))), true), true, is_a_theorem(implies(falsehood, implies(Z6, W6))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 192.82/32.58  = { by axiom 1 (ifeq_axiom) }
% 192.82/32.58    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W6, falsehood), implies(Z6, falsehood)), implies(falsehood, S6)), implies(T6, implies(falsehood, S6)))), true, is_a_theorem(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6))), true), true, is_a_theorem(implies(falsehood, implies(Z6, W6))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 192.82/32.59  = { by axiom 1 (ifeq_axiom) R->L }
% 192.82/32.59    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(W6, falsehood), implies(Z6, falsehood)), implies(falsehood, S6)), implies(T6, implies(falsehood, S6)))), true, is_a_theorem(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6))), true), true), true, is_a_theorem(implies(falsehood, implies(Z6, W6))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 192.82/32.59  = { by axiom 3 (c0_CAMeredith) R->L }
% 193.43/32.60    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(W6, falsehood), implies(Z6, falsehood)), implies(falsehood, S6)), implies(T6, implies(falsehood, S6))), implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(W6, falsehood), implies(Z6, falsehood)), implies(falsehood, S6)), implies(T6, implies(falsehood, S6)))), true, is_a_theorem(implies(implies(implies(T6, implies(falsehood, S6)), W6), implies(Z6, W6))), true), true), true, is_a_theorem(implies(falsehood, implies(Z6, W6))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 193.43/32.60  = { by axiom 2 (condensed_detachment) }
% 193.43/32.61    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(falsehood, implies(Z6, W6))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 193.43/32.61  = { by axiom 1 (ifeq_axiom) }
% 193.43/32.62    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z6, W6)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood))))), true, ifeq(is_a_theorem(implies(falsehood, implies(Z6, W6))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 193.43/32.62  = { by axiom 2 (condensed_detachment) }
% 193.43/32.62    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 193.43/32.63  = { by axiom 1 (ifeq_axiom) }
% 193.43/32.63    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 193.43/32.63  = { by axiom 1 (ifeq_axiom) R->L }
% 193.43/32.63    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 193.43/32.63  = { by axiom 3 (c0_CAMeredith) R->L }
% 193.43/32.64    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), Y6), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, T5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 193.43/32.64  = { by axiom 2 (condensed_detachment) }
% 193.43/32.64    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 193.43/32.64  = { by axiom 1 (ifeq_axiom) }
% 193.43/32.65    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 193.43/32.65  = { by axiom 1 (ifeq_axiom) R->L }
% 193.43/32.65    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 193.43/32.65  = { by axiom 3 (c0_CAMeredith) R->L }
% 193.43/32.65    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), falsehood)), implies(implies(falsehood, T5), falsehood)), implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, V5), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 193.43/32.65  = { by axiom 2 (condensed_detachment) }
% 193.43/32.66    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 193.43/32.66  = { by axiom 1 (ifeq_axiom) }
% 193.43/32.66    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 193.43/32.66  = { by axiom 1 (ifeq_axiom) R->L }
% 193.43/32.66    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 193.43/32.66  = { by axiom 3 (c0_CAMeredith) R->L }
% 193.43/32.66    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), U5), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 193.43/32.66  = { by axiom 2 (condensed_detachment) }
% 193.43/32.66    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 193.43/32.66  = { by axiom 1 (ifeq_axiom) }
% 193.43/32.67    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 193.43/32.67  = { by axiom 1 (ifeq_axiom) R->L }
% 193.43/32.67    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 193.43/32.67  = { by axiom 2 (condensed_detachment) R->L }
% 193.43/32.67    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 193.43/32.67  = { by axiom 3 (c0_CAMeredith) }
% 193.43/32.67    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 193.43/32.67  = { by axiom 1 (ifeq_axiom) }
% 193.43/32.68    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 193.43/32.68  = { by axiom 1 (ifeq_axiom) R->L }
% 193.43/32.68    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 193.43/32.69  = { by axiom 2 (condensed_detachment) R->L }
% 193.43/32.69    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))))), true, ifeq(is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 193.43/32.69  = { by axiom 1 (ifeq_axiom) R->L }
% 193.43/32.70    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.05/32.70  = { by axiom 2 (condensed_detachment) R->L }
% 194.05/32.71    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), V7), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), V7), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.05/32.71  = { by axiom 3 (c0_CAMeredith) }
% 194.05/32.72    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), V7), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.05/32.72  = { by axiom 1 (ifeq_axiom) }
% 194.05/32.73    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), V7), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.05/32.73  = { by axiom 1 (ifeq_axiom) R->L }
% 194.05/32.74    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), V7), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.05/32.74  = { by axiom 2 (condensed_detachment) R->L }
% 194.05/32.75    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), V7), falsehood)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), V7), implies(falsehood, falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), V7), falsehood)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), V7), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), V7), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.05/32.75  = { by axiom 3 (c0_CAMeredith) }
% 194.05/32.76    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), V7), falsehood)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), V7), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), V7), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.05/32.76  = { by axiom 1 (ifeq_axiom) }
% 194.05/32.77    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), V7), falsehood)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), V7), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), V7), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.05/32.77  = { by axiom 3 (c0_CAMeredith) }
% 194.05/32.78    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), V7), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), V7), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.05/32.78  = { by axiom 1 (ifeq_axiom) }
% 194.05/32.79    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), V7), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), V7), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.05/32.79  = { by axiom 1 (ifeq_axiom) R->L }
% 194.05/32.80    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), V7), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), V7), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.66/32.80  = { by axiom 3 (c0_CAMeredith) R->L }
% 194.66/32.81    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), V7), implies(falsehood, falsehood))), implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), V7), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), V7), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), V7), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.66/32.81  = { by axiom 2 (condensed_detachment) }
% 194.66/32.81    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.66/32.82  = { by axiom 1 (ifeq_axiom) }
% 194.66/32.82    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.66/32.83  = { by axiom 1 (ifeq_axiom) R->L }
% 194.66/32.83    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.66/32.83  = { by axiom 3 (c0_CAMeredith) R->L }
% 194.66/32.83    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), U7), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.66/32.84  = { by axiom 2 (condensed_detachment) }
% 194.66/32.84    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))))), true, ifeq(true, true, is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.66/32.84  = { by axiom 1 (ifeq_axiom) }
% 194.66/32.84    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))))), true, is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.66/32.85  = { by axiom 1 (ifeq_axiom) R->L }
% 194.66/32.85    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.66/32.85  = { by axiom 3 (c0_CAMeredith) R->L }
% 194.66/32.85    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(falsehood, Y7), falsehood)), implies(implies(falsehood, implies(Z7, W7)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))))), true), true, is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.66/32.85  = { by axiom 1 (ifeq_axiom) R->L }
% 194.66/32.86    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(falsehood, Y7), falsehood)), implies(implies(falsehood, implies(Z7, W7)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.66/32.86  = { by axiom 3 (c0_CAMeredith) R->L }
% 194.66/32.86    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(falsehood, Y7), falsehood)), implies(implies(falsehood, implies(Z7, W7)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), implies(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(falsehood, Y7), falsehood)), implies(implies(falsehood, implies(Z7, W7)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.66/32.86  = { by axiom 2 (condensed_detachment) }
% 194.66/32.86    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.66/32.87  = { by axiom 1 (ifeq_axiom) }
% 194.66/32.87    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.66/32.87  = { by axiom 1 (ifeq_axiom) R->L }
% 194.66/32.87    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.66/32.87  = { by axiom 2 (condensed_detachment) R->L }
% 194.66/32.87    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7)), implies(falsehood, implies(Z7, W7)))), true, ifeq(is_a_theorem(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7))), true, is_a_theorem(implies(falsehood, implies(Z7, W7))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.66/32.88  = { by axiom 1 (ifeq_axiom) R->L }
% 194.66/32.88    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7)), implies(falsehood, implies(Z7, W7)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7))), true, is_a_theorem(implies(falsehood, implies(Z7, W7))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.66/32.88  = { by axiom 2 (condensed_detachment) R->L }
% 194.66/32.88    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(W7, falsehood), implies(implies(T7, implies(falsehood, S7)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Z7, W7), X8), implies(falsehood, falsehood))), implies(implies(implies(implies(implies(Z7, W7), X8), implies(falsehood, falsehood)), W7), implies(implies(T7, implies(falsehood, S7)), W7)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(W7, falsehood), implies(implies(T7, implies(falsehood, S7)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Z7, W7), X8), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(Z7, W7), X8), implies(falsehood, falsehood)), W7), implies(implies(T7, implies(falsehood, S7)), W7))), true), true), true, is_a_theorem(implies(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7)), implies(falsehood, implies(Z7, W7)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7))), true, is_a_theorem(implies(falsehood, implies(Z7, W7))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.66/32.88  = { by axiom 3 (c0_CAMeredith) }
% 194.66/32.88    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(W7, falsehood), implies(implies(T7, implies(falsehood, S7)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Z7, W7), X8), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(Z7, W7), X8), implies(falsehood, falsehood)), W7), implies(implies(T7, implies(falsehood, S7)), W7))), true), true), true, is_a_theorem(implies(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7)), implies(falsehood, implies(Z7, W7)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7))), true, is_a_theorem(implies(falsehood, implies(Z7, W7))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.66/32.89  = { by axiom 1 (ifeq_axiom) }
% 194.66/32.89    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W7, falsehood), implies(implies(T7, implies(falsehood, S7)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Z7, W7), X8), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(Z7, W7), X8), implies(falsehood, falsehood)), W7), implies(implies(T7, implies(falsehood, S7)), W7))), true), true, is_a_theorem(implies(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7)), implies(falsehood, implies(Z7, W7)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7))), true, is_a_theorem(implies(falsehood, implies(Z7, W7))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.66/32.89  = { by axiom 1 (ifeq_axiom) R->L }
% 194.66/32.89    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W7, falsehood), implies(implies(T7, implies(falsehood, S7)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Z7, W7), X8), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(Z7, W7), X8), implies(falsehood, falsehood)), W7), implies(implies(T7, implies(falsehood, S7)), W7))), true), true, is_a_theorem(implies(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7)), implies(falsehood, implies(Z7, W7)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7))), true, is_a_theorem(implies(falsehood, implies(Z7, W7))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.66/32.89  = { by axiom 3 (c0_CAMeredith) R->L }
% 194.66/32.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(T7, implies(falsehood, S7)), falsehood)), implies(implies(implies(Z7, W7), X8), falsehood)), W7), implies(implies(W7, falsehood), implies(implies(T7, implies(falsehood, S7)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(W7, falsehood), implies(implies(T7, implies(falsehood, S7)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Z7, W7), X8), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(Z7, W7), X8), implies(falsehood, falsehood)), W7), implies(implies(T7, implies(falsehood, S7)), W7))), true), true, is_a_theorem(implies(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7)), implies(falsehood, implies(Z7, W7)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7))), true, is_a_theorem(implies(falsehood, implies(Z7, W7))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 194.66/32.90  = { by axiom 1 (ifeq_axiom) R->L }
% 195.26/32.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(T7, implies(falsehood, S7)), falsehood)), implies(implies(implies(Z7, W7), X8), falsehood)), W7), implies(implies(W7, falsehood), implies(implies(T7, implies(falsehood, S7)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(W7, falsehood), implies(implies(T7, implies(falsehood, S7)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Z7, W7), X8), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(Z7, W7), X8), implies(falsehood, falsehood)), W7), implies(implies(T7, implies(falsehood, S7)), W7))), true), true, is_a_theorem(implies(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7)), implies(falsehood, implies(Z7, W7)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7))), true, is_a_theorem(implies(falsehood, implies(Z7, W7))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/32.90  = { by axiom 3 (c0_CAMeredith) R->L }
% 195.26/32.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(T7, implies(falsehood, S7)), falsehood)), implies(implies(implies(Z7, W7), X8), falsehood)), W7), implies(implies(W7, falsehood), implies(implies(T7, implies(falsehood, S7)), falsehood))), implies(implies(implies(implies(W7, falsehood), implies(implies(T7, implies(falsehood, S7)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Z7, W7), X8), implies(falsehood, falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(T7, implies(falsehood, S7)), falsehood)), implies(implies(implies(Z7, W7), X8), falsehood)), W7), implies(implies(W7, falsehood), implies(implies(T7, implies(falsehood, S7)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(W7, falsehood), implies(implies(T7, implies(falsehood, S7)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(Z7, W7), X8), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(Z7, W7), X8), implies(falsehood, falsehood)), W7), implies(implies(T7, implies(falsehood, S7)), W7))), true), true, is_a_theorem(implies(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7)), implies(falsehood, implies(Z7, W7)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7))), true, is_a_theorem(implies(falsehood, implies(Z7, W7))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/32.90  = { by axiom 2 (condensed_detachment) }
% 195.26/32.91    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(Z7, W7), X8), implies(falsehood, falsehood)), W7), implies(implies(T7, implies(falsehood, S7)), W7))), true), true, is_a_theorem(implies(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7)), implies(falsehood, implies(Z7, W7)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7))), true, is_a_theorem(implies(falsehood, implies(Z7, W7))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/32.91  = { by axiom 1 (ifeq_axiom) }
% 195.26/32.91    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z7, W7), X8), implies(falsehood, falsehood)), W7), implies(implies(T7, implies(falsehood, S7)), W7))), true, is_a_theorem(implies(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7)), implies(falsehood, implies(Z7, W7)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7))), true, is_a_theorem(implies(falsehood, implies(Z7, W7))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/32.91  = { by axiom 1 (ifeq_axiom) R->L }
% 195.26/32.91    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z7, W7), X8), implies(falsehood, falsehood)), W7), implies(implies(T7, implies(falsehood, S7)), W7))), true, is_a_theorem(implies(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7)), implies(falsehood, implies(Z7, W7)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7))), true, is_a_theorem(implies(falsehood, implies(Z7, W7))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/32.91  = { by axiom 3 (c0_CAMeredith) R->L }
% 195.26/32.92    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(Z7, W7), X8), implies(falsehood, falsehood)), W7), implies(implies(T7, implies(falsehood, S7)), W7)), implies(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7)), implies(falsehood, implies(Z7, W7))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z7, W7), X8), implies(falsehood, falsehood)), W7), implies(implies(T7, implies(falsehood, S7)), W7))), true, is_a_theorem(implies(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7)), implies(falsehood, implies(Z7, W7)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7))), true, is_a_theorem(implies(falsehood, implies(Z7, W7))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/32.92  = { by axiom 2 (condensed_detachment) }
% 195.26/32.92    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7))), true, is_a_theorem(implies(falsehood, implies(Z7, W7))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/32.92  = { by axiom 1 (ifeq_axiom) }
% 195.26/32.92    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7))), true, is_a_theorem(implies(falsehood, implies(Z7, W7))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/32.92  = { by axiom 1 (ifeq_axiom) R->L }
% 195.26/32.92    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7))), true), true, is_a_theorem(implies(falsehood, implies(Z7, W7))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/32.93  = { by axiom 2 (condensed_detachment) R->L }
% 195.26/32.93    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, S7), implies(Z7, falsehood)), implies(T7, falsehood)), W7), implies(implies(W7, falsehood), implies(Z7, falsehood))), implies(implies(implies(implies(W7, falsehood), implies(Z7, falsehood)), implies(falsehood, S7)), implies(T7, implies(falsehood, S7))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S7), implies(Z7, falsehood)), implies(T7, falsehood)), W7), implies(implies(W7, falsehood), implies(Z7, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(W7, falsehood), implies(Z7, falsehood)), implies(falsehood, S7)), implies(T7, implies(falsehood, S7)))), true), true), true, is_a_theorem(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7))), true), true, is_a_theorem(implies(falsehood, implies(Z7, W7))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/32.93  = { by axiom 3 (c0_CAMeredith) }
% 195.26/32.93    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S7), implies(Z7, falsehood)), implies(T7, falsehood)), W7), implies(implies(W7, falsehood), implies(Z7, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(W7, falsehood), implies(Z7, falsehood)), implies(falsehood, S7)), implies(T7, implies(falsehood, S7)))), true), true), true, is_a_theorem(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7))), true), true, is_a_theorem(implies(falsehood, implies(Z7, W7))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/32.93  = { by axiom 1 (ifeq_axiom) }
% 195.26/32.93    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S7), implies(Z7, falsehood)), implies(T7, falsehood)), W7), implies(implies(W7, falsehood), implies(Z7, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(W7, falsehood), implies(Z7, falsehood)), implies(falsehood, S7)), implies(T7, implies(falsehood, S7)))), true), true, is_a_theorem(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7))), true), true, is_a_theorem(implies(falsehood, implies(Z7, W7))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/32.94  = { by axiom 3 (c0_CAMeredith) }
% 195.26/32.94    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W7, falsehood), implies(Z7, falsehood)), implies(falsehood, S7)), implies(T7, implies(falsehood, S7)))), true), true, is_a_theorem(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7))), true), true, is_a_theorem(implies(falsehood, implies(Z7, W7))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/32.94  = { by axiom 1 (ifeq_axiom) }
% 195.26/32.94    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W7, falsehood), implies(Z7, falsehood)), implies(falsehood, S7)), implies(T7, implies(falsehood, S7)))), true, is_a_theorem(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7))), true), true, is_a_theorem(implies(falsehood, implies(Z7, W7))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/32.94  = { by axiom 1 (ifeq_axiom) R->L }
% 195.26/32.94    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(W7, falsehood), implies(Z7, falsehood)), implies(falsehood, S7)), implies(T7, implies(falsehood, S7)))), true, is_a_theorem(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7))), true), true), true, is_a_theorem(implies(falsehood, implies(Z7, W7))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/32.94  = { by axiom 3 (c0_CAMeredith) R->L }
% 195.26/32.95    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(W7, falsehood), implies(Z7, falsehood)), implies(falsehood, S7)), implies(T7, implies(falsehood, S7))), implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(W7, falsehood), implies(Z7, falsehood)), implies(falsehood, S7)), implies(T7, implies(falsehood, S7)))), true, is_a_theorem(implies(implies(implies(T7, implies(falsehood, S7)), W7), implies(Z7, W7))), true), true), true, is_a_theorem(implies(falsehood, implies(Z7, W7))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/32.95  = { by axiom 2 (condensed_detachment) }
% 195.26/32.95    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(falsehood, implies(Z7, W7))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/32.95  = { by axiom 1 (ifeq_axiom) }
% 195.26/32.95    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(Z7, W7)), implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true, ifeq(is_a_theorem(implies(falsehood, implies(Z7, W7))), true, is_a_theorem(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/32.95  = { by axiom 2 (condensed_detachment) }
% 195.26/32.95    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/32.95  = { by axiom 1 (ifeq_axiom) }
% 195.26/32.95    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/32.95  = { by axiom 1 (ifeq_axiom) R->L }
% 195.26/32.95    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/32.95  = { by axiom 3 (c0_CAMeredith) R->L }
% 195.26/32.95    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Y7), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), falsehood), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/32.96  = { by axiom 2 (condensed_detachment) }
% 195.26/32.96    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/32.96  = { by axiom 1 (ifeq_axiom) }
% 195.26/32.96    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/32.96  = { by axiom 1 (ifeq_axiom) R->L }
% 195.26/32.96    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/32.96  = { by axiom 2 (condensed_detachment) R->L }
% 195.26/32.96    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/32.96  = { by axiom 3 (c0_CAMeredith) }
% 195.26/32.96    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/32.97  = { by axiom 1 (ifeq_axiom) }
% 195.26/32.97    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/32.97  = { by axiom 1 (ifeq_axiom) R->L }
% 195.26/32.97    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/32.97  = { by axiom 2 (condensed_detachment) R->L }
% 195.26/32.97    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/32.97  = { by axiom 3 (c0_CAMeredith) }
% 195.26/32.97    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/32.98  = { by axiom 1 (ifeq_axiom) }
% 195.26/32.98    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/32.98  = { by axiom 1 (ifeq_axiom) R->L }
% 195.26/32.98    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/32.98  = { by axiom 2 (condensed_detachment) R->L }
% 195.26/32.99    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/32.99  = { by axiom 3 (c0_CAMeredith) }
% 195.26/32.99    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/33.00  = { by axiom 1 (ifeq_axiom) }
% 195.26/33.00    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/33.00  = { by axiom 1 (ifeq_axiom) R->L }
% 195.26/33.01    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/33.01  = { by axiom 2 (condensed_detachment) R->L }
% 195.26/33.01    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true, ifeq(is_a_theorem(implies(falsehood, implies(U8, T8))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/33.02  = { by axiom 1 (ifeq_axiom) R->L }
% 195.26/33.02    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(falsehood, implies(U8, T8))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 195.26/33.03  = { by axiom 2 (condensed_detachment) R->L }
% 196.07/33.03    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T8, falsehood), implies(U8, falsehood)), implies(falsehood, S8)), implies(X9, implies(falsehood, S8))), implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(T8, falsehood), implies(U8, falsehood)), implies(falsehood, S8)), implies(X9, implies(falsehood, S8)))), true, is_a_theorem(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8))), true), true), true, is_a_theorem(implies(falsehood, implies(U8, T8))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 196.07/33.04  = { by axiom 3 (c0_CAMeredith) }
% 196.07/33.04    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(T8, falsehood), implies(U8, falsehood)), implies(falsehood, S8)), implies(X9, implies(falsehood, S8)))), true, is_a_theorem(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8))), true), true), true, is_a_theorem(implies(falsehood, implies(U8, T8))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 196.07/33.04  = { by axiom 1 (ifeq_axiom) }
% 196.07/33.05    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T8, falsehood), implies(U8, falsehood)), implies(falsehood, S8)), implies(X9, implies(falsehood, S8)))), true, is_a_theorem(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8))), true), true, is_a_theorem(implies(falsehood, implies(U8, T8))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 196.07/33.05  = { by axiom 1 (ifeq_axiom) R->L }
% 196.07/33.06    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T8, falsehood), implies(U8, falsehood)), implies(falsehood, S8)), implies(X9, implies(falsehood, S8)))), true), true, is_a_theorem(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8))), true), true, is_a_theorem(implies(falsehood, implies(U8, T8))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 196.07/33.06  = { by axiom 3 (c0_CAMeredith) R->L }
% 196.07/33.06    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S8), implies(U8, falsehood)), implies(X9, falsehood)), T8), implies(implies(T8, falsehood), implies(U8, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(T8, falsehood), implies(U8, falsehood)), implies(falsehood, S8)), implies(X9, implies(falsehood, S8)))), true), true, is_a_theorem(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8))), true), true, is_a_theorem(implies(falsehood, implies(U8, T8))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 196.07/33.07  = { by axiom 1 (ifeq_axiom) R->L }
% 196.07/33.07    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S8), implies(U8, falsehood)), implies(X9, falsehood)), T8), implies(implies(T8, falsehood), implies(U8, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(T8, falsehood), implies(U8, falsehood)), implies(falsehood, S8)), implies(X9, implies(falsehood, S8)))), true), true), true, is_a_theorem(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8))), true), true, is_a_theorem(implies(falsehood, implies(U8, T8))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 196.07/33.08  = { by axiom 3 (c0_CAMeredith) R->L }
% 196.07/33.08    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, S8), implies(U8, falsehood)), implies(X9, falsehood)), T8), implies(implies(T8, falsehood), implies(U8, falsehood))), implies(implies(implies(implies(T8, falsehood), implies(U8, falsehood)), implies(falsehood, S8)), implies(X9, implies(falsehood, S8))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S8), implies(U8, falsehood)), implies(X9, falsehood)), T8), implies(implies(T8, falsehood), implies(U8, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(T8, falsehood), implies(U8, falsehood)), implies(falsehood, S8)), implies(X9, implies(falsehood, S8)))), true), true), true, is_a_theorem(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8))), true), true, is_a_theorem(implies(falsehood, implies(U8, T8))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 196.07/33.09  = { by axiom 2 (condensed_detachment) }
% 196.07/33.09    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8))), true), true, is_a_theorem(implies(falsehood, implies(U8, T8))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 196.07/33.09  = { by axiom 1 (ifeq_axiom) }
% 196.07/33.10    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8))), true, is_a_theorem(implies(falsehood, implies(U8, T8))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 196.07/33.10  = { by axiom 1 (ifeq_axiom) R->L }
% 196.07/33.11    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8))), true, is_a_theorem(implies(falsehood, implies(U8, T8))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 196.07/33.11  = { by axiom 2 (condensed_detachment) R->L }
% 196.07/33.12    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(U8, T8), Y9), implies(falsehood, falsehood)), T8), implies(implies(X9, implies(falsehood, S8)), T8)), implies(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8)), implies(falsehood, implies(U8, T8))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(U8, T8), Y9), implies(falsehood, falsehood)), T8), implies(implies(X9, implies(falsehood, S8)), T8))), true, is_a_theorem(implies(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8)), implies(falsehood, implies(U8, T8)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8))), true, is_a_theorem(implies(falsehood, implies(U8, T8))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 196.07/33.12  = { by axiom 3 (c0_CAMeredith) }
% 196.07/33.12    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(U8, T8), Y9), implies(falsehood, falsehood)), T8), implies(implies(X9, implies(falsehood, S8)), T8))), true, is_a_theorem(implies(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8)), implies(falsehood, implies(U8, T8)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8))), true, is_a_theorem(implies(falsehood, implies(U8, T8))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 196.07/33.13  = { by axiom 1 (ifeq_axiom) }
% 196.70/33.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(U8, T8), Y9), implies(falsehood, falsehood)), T8), implies(implies(X9, implies(falsehood, S8)), T8))), true, is_a_theorem(implies(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8)), implies(falsehood, implies(U8, T8)))), true), true, ifeq(is_a_theorem(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8))), true, is_a_theorem(implies(falsehood, implies(U8, T8))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 196.70/33.14  = { by axiom 1 (ifeq_axiom) R->L }
% 196.70/33.14    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(U8, T8), Y9), implies(falsehood, falsehood)), T8), implies(implies(X9, implies(falsehood, S8)), T8))), true), true, is_a_theorem(implies(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8)), implies(falsehood, implies(U8, T8)))), true), true, ifeq(is_a_theorem(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8))), true, is_a_theorem(implies(falsehood, implies(U8, T8))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 196.70/33.15  = { by axiom 2 (condensed_detachment) R->L }
% 196.70/33.16    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(X9, implies(falsehood, S8)), falsehood)), implies(implies(implies(U8, T8), Y9), falsehood)), T8), implies(implies(T8, falsehood), implies(implies(X9, implies(falsehood, S8)), falsehood))), implies(implies(implies(implies(T8, falsehood), implies(implies(X9, implies(falsehood, S8)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(U8, T8), Y9), implies(falsehood, falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(X9, implies(falsehood, S8)), falsehood)), implies(implies(implies(U8, T8), Y9), falsehood)), T8), implies(implies(T8, falsehood), implies(implies(X9, implies(falsehood, S8)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(T8, falsehood), implies(implies(X9, implies(falsehood, S8)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(U8, T8), Y9), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(U8, T8), Y9), implies(falsehood, falsehood)), T8), implies(implies(X9, implies(falsehood, S8)), T8))), true), true, is_a_theorem(implies(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8)), implies(falsehood, implies(U8, T8)))), true), true, ifeq(is_a_theorem(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8))), true, is_a_theorem(implies(falsehood, implies(U8, T8))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 196.70/33.17  = { by axiom 3 (c0_CAMeredith) }
% 196.70/33.17    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(X9, implies(falsehood, S8)), falsehood)), implies(implies(implies(U8, T8), Y9), falsehood)), T8), implies(implies(T8, falsehood), implies(implies(X9, implies(falsehood, S8)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(T8, falsehood), implies(implies(X9, implies(falsehood, S8)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(U8, T8), Y9), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(U8, T8), Y9), implies(falsehood, falsehood)), T8), implies(implies(X9, implies(falsehood, S8)), T8))), true), true, is_a_theorem(implies(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8)), implies(falsehood, implies(U8, T8)))), true), true, ifeq(is_a_theorem(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8))), true, is_a_theorem(implies(falsehood, implies(U8, T8))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 196.70/33.18  = { by axiom 1 (ifeq_axiom) }
% 196.70/33.18    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(X9, implies(falsehood, S8)), falsehood)), implies(implies(implies(U8, T8), Y9), falsehood)), T8), implies(implies(T8, falsehood), implies(implies(X9, implies(falsehood, S8)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(T8, falsehood), implies(implies(X9, implies(falsehood, S8)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(U8, T8), Y9), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(U8, T8), Y9), implies(falsehood, falsehood)), T8), implies(implies(X9, implies(falsehood, S8)), T8))), true), true, is_a_theorem(implies(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8)), implies(falsehood, implies(U8, T8)))), true), true, ifeq(is_a_theorem(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8))), true, is_a_theorem(implies(falsehood, implies(U8, T8))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 196.70/33.19  = { by axiom 3 (c0_CAMeredith) }
% 196.70/33.19    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T8, falsehood), implies(implies(X9, implies(falsehood, S8)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(U8, T8), Y9), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(U8, T8), Y9), implies(falsehood, falsehood)), T8), implies(implies(X9, implies(falsehood, S8)), T8))), true), true, is_a_theorem(implies(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8)), implies(falsehood, implies(U8, T8)))), true), true, ifeq(is_a_theorem(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8))), true, is_a_theorem(implies(falsehood, implies(U8, T8))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 196.70/33.20  = { by axiom 1 (ifeq_axiom) }
% 197.09/33.20    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T8, falsehood), implies(implies(X9, implies(falsehood, S8)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(U8, T8), Y9), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(U8, T8), Y9), implies(falsehood, falsehood)), T8), implies(implies(X9, implies(falsehood, S8)), T8))), true), true, is_a_theorem(implies(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8)), implies(falsehood, implies(U8, T8)))), true), true, ifeq(is_a_theorem(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8))), true, is_a_theorem(implies(falsehood, implies(U8, T8))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 197.09/33.20  = { by axiom 1 (ifeq_axiom) R->L }
% 197.09/33.21    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(T8, falsehood), implies(implies(X9, implies(falsehood, S8)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(U8, T8), Y9), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(U8, T8), Y9), implies(falsehood, falsehood)), T8), implies(implies(X9, implies(falsehood, S8)), T8))), true), true), true, is_a_theorem(implies(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8)), implies(falsehood, implies(U8, T8)))), true), true, ifeq(is_a_theorem(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8))), true, is_a_theorem(implies(falsehood, implies(U8, T8))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 197.09/33.21  = { by axiom 3 (c0_CAMeredith) R->L }
% 197.09/33.22    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T8, falsehood), implies(implies(X9, implies(falsehood, S8)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(U8, T8), Y9), implies(falsehood, falsehood))), implies(implies(implies(implies(implies(U8, T8), Y9), implies(falsehood, falsehood)), T8), implies(implies(X9, implies(falsehood, S8)), T8)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(T8, falsehood), implies(implies(X9, implies(falsehood, S8)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(U8, T8), Y9), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(U8, T8), Y9), implies(falsehood, falsehood)), T8), implies(implies(X9, implies(falsehood, S8)), T8))), true), true), true, is_a_theorem(implies(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8)), implies(falsehood, implies(U8, T8)))), true), true, ifeq(is_a_theorem(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8))), true, is_a_theorem(implies(falsehood, implies(U8, T8))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 197.09/33.22  = { by axiom 2 (condensed_detachment) }
% 197.09/33.22    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8)), implies(falsehood, implies(U8, T8)))), true), true, ifeq(is_a_theorem(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8))), true, is_a_theorem(implies(falsehood, implies(U8, T8))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 197.09/33.23  = { by axiom 1 (ifeq_axiom) }
% 197.09/33.23    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8)), implies(falsehood, implies(U8, T8)))), true, ifeq(is_a_theorem(implies(implies(implies(X9, implies(falsehood, S8)), T8), implies(U8, T8))), true, is_a_theorem(implies(falsehood, implies(U8, T8))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 197.09/33.24  = { by axiom 2 (condensed_detachment) }
% 197.09/33.24    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 197.09/33.25  = { by axiom 1 (ifeq_axiom) }
% 197.09/33.26    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 197.09/33.27  = { by axiom 1 (ifeq_axiom) R->L }
% 197.09/33.27    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 197.09/33.28  = { by axiom 2 (condensed_detachment) R->L }
% 197.09/33.29    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), falsehood)), implies(implies(falsehood, implies(U8, T8)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), 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% 197.09/33.30  = { by axiom 3 (c0_CAMeredith) }
% 197.70/33.30    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, 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implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 197.70/33.31  = { by axiom 1 (ifeq_axiom) }
% 197.70/33.32    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), falsehood)), implies(implies(falsehood, implies(U8, T8)), falsehood)), falsehood), implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))))), true), true, is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 197.70/33.33  = { by axiom 3 (c0_CAMeredith) }
% 197.70/33.33    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))))), true), true, is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 197.70/33.35  = { by axiom 1 (ifeq_axiom) }
% 197.70/33.36    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))))), true, is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 197.70/33.37  = { by axiom 1 (ifeq_axiom) R->L }
% 197.70/33.38    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))))), true, ifeq(true, true, is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), 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is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), 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% 197.70/33.39  = { by axiom 2 (condensed_detachment) R->L }
% 198.32/33.40    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), 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falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), Z9), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), 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implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 198.32/33.42  = { by axiom 3 (c0_CAMeredith) }
% 198.32/33.43    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), Z9), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 198.32/33.45  = { by axiom 1 (ifeq_axiom) }
% 198.32/33.46    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), Z9), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(falsehood, 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implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 198.32/33.48  = { by axiom 1 (ifeq_axiom) R->L }
% 198.32/33.49    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), Z9), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), 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falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true), true, 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falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, 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implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 198.94/33.50  = { by axiom 2 (condensed_detachment) R->L }
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% 198.94/33.54  = { by axiom 3 (c0_CAMeredith) }
% 198.94/33.55    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), 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implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, 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implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 198.94/33.57  = { by axiom 1 (ifeq_axiom) }
% 198.94/33.58    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), Z9), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), W9), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), W9), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), Z9), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), Z9), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 199.52/33.62  = { by axiom 1 (ifeq_axiom) R->L }
% 199.52/33.64    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), 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falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), 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implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 199.52/33.67  = { by axiom 3 (c0_CAMeredith) R->L }
% 199.52/33.68    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), 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% 200.15/33.70  = { by axiom 1 (ifeq_axiom) R->L }
% 200.15/33.71    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), 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implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), 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% 200.15/33.73  = { by axiom 3 (c0_CAMeredith) R->L }
% 200.15/33.75    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), 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% 200.15/33.77  = { by axiom 2 (condensed_detachment) }
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true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 200.15/33.79  = { by axiom 1 (ifeq_axiom) }
% 200.74/33.80    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), 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falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), W9), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), falsehood)), 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is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, 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true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 200.74/33.81  = { by axiom 1 (ifeq_axiom) R->L }
% 200.74/33.83    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), 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falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), W9), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), Z9), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), Z9), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, 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is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), 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falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, 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a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 200.74/33.83  = { by axiom 3 (c0_CAMeredith) R->L }
% 200.74/33.84    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), W9), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), Z9), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), Z9), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), W9), implies(falsehood, falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), Z9), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), Z9), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 200.74/33.85  = { by axiom 2 (condensed_detachment) }
% 200.74/33.85    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true), true, is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 200.74/33.86  = { by axiom 1 (ifeq_axiom) }
% 200.74/33.86    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))))), true, ifeq(is_a_theorem(implies(implies(implies(falsehood, implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true, is_a_theorem(implies(implies(falsehood, implies(U8, T8)), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 200.74/33.87  = { by axiom 2 (condensed_detachment) }
% 200.74/33.87    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 200.74/33.87  = { by axiom 1 (ifeq_axiom) }
% 200.74/33.88    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 200.74/33.88  = { by axiom 1 (ifeq_axiom) R->L }
% 200.74/33.88    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 200.74/33.88  = { by axiom 3 (c0_CAMeredith) R->L }
% 200.74/33.89    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), V8), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 200.74/33.89  = { by axiom 2 (condensed_detachment) }
% 200.74/33.89    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 200.74/33.89  = { by axiom 1 (ifeq_axiom) }
% 200.74/33.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 201.35/33.90  = { by axiom 1 (ifeq_axiom) R->L }
% 201.35/33.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 201.35/33.90  = { by axiom 2 (condensed_detachment) R->L }
% 201.35/33.91    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)), Z8), implies(falsehood, Z8)), implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)), Z8), implies(falsehood, Z8))), true, is_a_theorem(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 201.35/33.91  = { by axiom 3 (c0_CAMeredith) }
% 201.35/33.91    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)), Z8), implies(falsehood, Z8))), true, is_a_theorem(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 201.35/33.91  = { by axiom 1 (ifeq_axiom) }
% 201.35/33.92    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)), Z8), implies(falsehood, Z8))), true, is_a_theorem(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 201.35/33.92  = { by axiom 1 (ifeq_axiom) R->L }
% 201.35/33.92    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)), Z8), implies(falsehood, Z8))), true), true, is_a_theorem(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 201.35/33.93  = { by axiom 2 (condensed_detachment) R->L }
% 201.35/33.93    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), falsehood)), implies(falsehood, falsehood)), implies(implies(Z8, U9), implies(falsehood, falsehood))), implies(implies(implies(implies(Z8, U9), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), falsehood)), implies(falsehood, falsehood)), implies(implies(Z8, U9), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Z8, U9), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)), Z8), implies(falsehood, Z8))), true), true, is_a_theorem(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 201.35/33.93  = { by axiom 3 (c0_CAMeredith) }
% 201.35/33.93    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), falsehood)), implies(falsehood, falsehood)), implies(implies(Z8, U9), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Z8, U9), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)), Z8), implies(falsehood, Z8))), true), true, is_a_theorem(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 201.35/33.94  = { by axiom 1 (ifeq_axiom) }
% 201.35/33.94    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), falsehood)), implies(falsehood, falsehood)), implies(implies(Z8, U9), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Z8, U9), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)), Z8), implies(falsehood, Z8))), true), true, is_a_theorem(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 201.35/33.94  = { by axiom 1 (ifeq_axiom) R->L }
% 201.35/33.95    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), falsehood)), implies(falsehood, falsehood)), implies(implies(Z8, U9), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(Z8, U9), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)), Z8), implies(falsehood, Z8))), true), true, is_a_theorem(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 201.35/33.95  = { by axiom 3 (c0_CAMeredith) R->L }
% 201.35/33.95    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), falsehood)), implies(implies(Z8, U9), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), falsehood)), implies(falsehood, falsehood)), implies(implies(Z8, U9), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(Z8, U9), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)), Z8), implies(falsehood, Z8))), true), true, is_a_theorem(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 201.35/33.96  = { by axiom 1 (ifeq_axiom) R->L }
% 201.35/33.96    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), falsehood)), implies(implies(Z8, U9), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), falsehood)), implies(falsehood, falsehood)), implies(implies(Z8, U9), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z8, U9), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)), Z8), implies(falsehood, Z8))), true), true, is_a_theorem(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 201.35/33.96  = { by axiom 3 (c0_CAMeredith) R->L }
% 201.35/33.96    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), falsehood)), implies(implies(Z8, U9), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), falsehood)), implies(falsehood, falsehood)), implies(implies(Z8, U9), implies(falsehood, falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), falsehood)), implies(implies(Z8, U9), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)), implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood), falsehood), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), falsehood)), implies(falsehood, falsehood)), implies(implies(Z8, U9), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z8, U9), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)), Z8), implies(falsehood, Z8))), true), true, is_a_theorem(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 201.35/33.97  = { by axiom 2 (condensed_detachment) }
% 201.35/33.97    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z8, U9), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)), Z8), implies(falsehood, Z8))), true), true, is_a_theorem(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 201.35/33.97  = { by axiom 1 (ifeq_axiom) }
% 201.35/33.97    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z8, U9), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)), Z8), implies(falsehood, Z8))), true), true, is_a_theorem(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 201.35/33.98  = { by axiom 1 (ifeq_axiom) R->L }
% 201.35/33.98    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Z8, U9), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)), Z8), implies(falsehood, Z8))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 201.35/33.98  = { by axiom 3 (c0_CAMeredith) R->L }
% 201.35/33.98    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z8, U9), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)), Z8), implies(falsehood, Z8)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z8, U9), implies(falsehood, falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), V9), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), falsehood)), Z8), implies(falsehood, Z8))), true), true), true, is_a_theorem(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 201.35/33.99  = { by axiom 2 (condensed_detachment) }
% 201.35/33.99    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 201.35/33.99  = { by axiom 1 (ifeq_axiom) }
% 201.35/33.99    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(falsehood, Z8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), falsehood)), implies(implies(falsehood, Z8), falsehood)), implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 201.35/33.99  = { by axiom 2 (condensed_detachment) }
% 201.35/33.99    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 201.35/33.99  = { by axiom 1 (ifeq_axiom) }
% 201.35/33.99    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 201.35/34.00  = { by axiom 1 (ifeq_axiom) R->L }
% 201.35/34.00    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 201.35/34.00  = { by axiom 3 (c0_CAMeredith) R->L }
% 201.35/34.00    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, implies(X, Y)), falsehood), W8), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood), Y8), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 201.35/34.00  = { by axiom 2 (condensed_detachment) }
% 201.35/34.00    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 201.35/34.00  = { by axiom 1 (ifeq_axiom) }
% 201.35/34.00    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(falsehood, S2), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood)), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 201.35/34.00  = { by axiom 2 (condensed_detachment) }
% 201.35/34.00    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 201.35/34.00  = { by axiom 1 (ifeq_axiom) }
% 201.35/34.00    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 201.35/34.00  = { by axiom 1 (ifeq_axiom) R->L }
% 201.35/34.00    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 201.35/34.00  = { by axiom 3 (c0_CAMeredith) R->L }
% 201.35/34.00    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a)), implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(falsehood, implies(X, Y)), falsehood)), falsehood), implies(implies(a, b), a))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a)))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 201.35/34.00  = { by axiom 2 (condensed_detachment) }
% 201.35/34.00    ifeq(ifeq(true, true, is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 201.35/34.00  = { by axiom 1 (ifeq_axiom) }
% 201.35/34.00    ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 201.35/34.00  = { by axiom 1 (ifeq_axiom) R->L }
% 201.35/34.00    ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 201.35/34.00  = { by axiom 2 (condensed_detachment) R->L }
% 201.35/34.00    ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true, ifeq(is_a_theorem(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 201.35/34.00  = { by axiom 1 (ifeq_axiom) R->L }
% 201.35/34.00    ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 201.35/34.00  = { by axiom 2 (condensed_detachment) R->L }
% 201.35/34.00    ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Y, falsehood), implies(implies(T9, implies(falsehood, S9)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(X, Y), X10), implies(falsehood, falsehood))), implies(implies(implies(implies(implies(X, Y), X10), implies(falsehood, falsehood)), Y), implies(implies(T9, implies(falsehood, S9)), Y)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(implies(T9, implies(falsehood, S9)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(X, Y), X10), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), X10), implies(falsehood, falsehood)), Y), implies(implies(T9, implies(falsehood, S9)), Y))), true), true), true, is_a_theorem(implies(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 201.35/34.00  = { by axiom 3 (c0_CAMeredith) }
% 201.35/34.00    ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(implies(T9, implies(falsehood, S9)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(X, Y), X10), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), X10), implies(falsehood, falsehood)), Y), implies(implies(T9, implies(falsehood, S9)), Y))), true), true), true, is_a_theorem(implies(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 201.35/34.01  = { by axiom 1 (ifeq_axiom) }
% 201.35/34.01    ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(implies(T9, implies(falsehood, S9)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(X, Y), X10), implies(falsehood, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), X10), implies(falsehood, falsehood)), Y), implies(implies(T9, implies(falsehood, S9)), Y))), true), true, is_a_theorem(implies(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 201.35/34.01  = { by axiom 1 (ifeq_axiom) R->L }
% 201.35/34.01    ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(implies(T9, implies(falsehood, S9)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(X, Y), X10), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), X10), implies(falsehood, falsehood)), Y), implies(implies(T9, implies(falsehood, S9)), Y))), true), true, is_a_theorem(implies(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 201.35/34.01  = { by axiom 3 (c0_CAMeredith) R->L }
% 201.35/34.01    ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(T9, implies(falsehood, S9)), falsehood)), implies(implies(implies(X, Y), X10), falsehood)), Y), implies(implies(Y, falsehood), implies(implies(T9, implies(falsehood, S9)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(implies(T9, implies(falsehood, S9)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(X, Y), X10), implies(falsehood, falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), X10), implies(falsehood, falsehood)), Y), implies(implies(T9, implies(falsehood, S9)), Y))), true), true, is_a_theorem(implies(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 201.35/34.01  = { by axiom 1 (ifeq_axiom) R->L }
% 201.35/34.01    ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(T9, implies(falsehood, S9)), falsehood)), implies(implies(implies(X, Y), X10), falsehood)), Y), implies(implies(Y, falsehood), implies(implies(T9, implies(falsehood, S9)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(implies(T9, implies(falsehood, S9)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(X, Y), X10), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), X10), implies(falsehood, falsehood)), Y), implies(implies(T9, implies(falsehood, S9)), Y))), true), true, is_a_theorem(implies(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 201.35/34.01  = { by axiom 3 (c0_CAMeredith) R->L }
% 201.35/34.01    ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(T9, implies(falsehood, S9)), falsehood)), implies(implies(implies(X, Y), X10), falsehood)), Y), implies(implies(Y, falsehood), implies(implies(T9, implies(falsehood, S9)), falsehood))), implies(implies(implies(implies(Y, falsehood), implies(implies(T9, implies(falsehood, S9)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(X, Y), X10), implies(falsehood, falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, falsehood), implies(implies(T9, implies(falsehood, S9)), falsehood)), implies(implies(implies(X, Y), X10), falsehood)), Y), implies(implies(Y, falsehood), implies(implies(T9, implies(falsehood, S9)), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(implies(T9, implies(falsehood, S9)), falsehood)), implies(falsehood, falsehood)), implies(implies(implies(X, Y), X10), implies(falsehood, falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), X10), implies(falsehood, falsehood)), Y), implies(implies(T9, implies(falsehood, S9)), Y))), true), true, is_a_theorem(implies(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 201.35/34.01  = { by axiom 2 (condensed_detachment) }
% 201.35/34.01    ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), X10), implies(falsehood, falsehood)), Y), implies(implies(T9, implies(falsehood, S9)), Y))), true), true, is_a_theorem(implies(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 201.35/34.01  = { by axiom 1 (ifeq_axiom) }
% 201.35/34.01    ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(X, Y), X10), implies(falsehood, falsehood)), Y), implies(implies(T9, implies(falsehood, S9)), Y))), true, is_a_theorem(implies(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true, ifeq(is_a_theorem(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 201.35/34.01  = { by axiom 1 (ifeq_axiom) R->L }
% 201.35/34.01    ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(X, Y), X10), implies(falsehood, falsehood)), Y), implies(implies(T9, implies(falsehood, S9)), Y))), true, is_a_theorem(implies(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 201.35/34.01  = { by axiom 3 (c0_CAMeredith) R->L }
% 201.35/34.01    ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), X10), implies(falsehood, falsehood)), Y), implies(implies(T9, implies(falsehood, S9)), Y)), implies(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y)), implies(falsehood, implies(X, Y))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(X, Y), X10), implies(falsehood, falsehood)), Y), implies(implies(T9, implies(falsehood, S9)), Y))), true, is_a_theorem(implies(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y)), implies(falsehood, implies(X, Y)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 201.35/34.01  = { by axiom 2 (condensed_detachment) }
% 201.35/34.01    ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 201.35/34.01  = { by axiom 1 (ifeq_axiom) }
% 201.35/34.01    ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y))), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 201.35/34.01  = { by axiom 1 (ifeq_axiom) R->L }
% 201.35/34.01    ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y))), true), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 201.35/34.01  = { by axiom 2 (condensed_detachment) R->L }
% 201.35/34.01    ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(falsehood, S9), implies(X, falsehood)), implies(T9, falsehood)), Y), implies(implies(Y, falsehood), implies(X, falsehood))), implies(implies(implies(implies(Y, falsehood), implies(X, falsehood)), implies(falsehood, S9)), implies(T9, implies(falsehood, S9))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S9), implies(X, falsehood)), implies(T9, falsehood)), Y), implies(implies(Y, falsehood), implies(X, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(X, falsehood)), implies(falsehood, S9)), implies(T9, implies(falsehood, S9)))), true), true), true, is_a_theorem(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y))), true), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 201.35/34.01  = { by axiom 3 (c0_CAMeredith) }
% 201.35/34.01    ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S9), implies(X, falsehood)), implies(T9, falsehood)), Y), implies(implies(Y, falsehood), implies(X, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(X, falsehood)), implies(falsehood, S9)), implies(T9, implies(falsehood, S9)))), true), true), true, is_a_theorem(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y))), true), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 201.35/34.01  = { by axiom 1 (ifeq_axiom) }
% 201.35/34.01    ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(falsehood, S9), implies(X, falsehood)), implies(T9, falsehood)), Y), implies(implies(Y, falsehood), implies(X, falsehood)))), true, is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(X, falsehood)), implies(falsehood, S9)), implies(T9, implies(falsehood, S9)))), true), true, is_a_theorem(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y))), true), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 201.35/34.01  = { by axiom 3 (c0_CAMeredith) }
% 201.35/34.01    ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(X, falsehood)), implies(falsehood, S9)), implies(T9, implies(falsehood, S9)))), true), true, is_a_theorem(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y))), true), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 201.35/34.01  = { by axiom 1 (ifeq_axiom) }
% 201.35/34.01    ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(X, falsehood)), implies(falsehood, S9)), implies(T9, implies(falsehood, S9)))), true, is_a_theorem(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y))), true), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 201.35/34.01  = { by axiom 1 (ifeq_axiom) R->L }
% 201.35/34.01    ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(X, falsehood)), implies(falsehood, S9)), implies(T9, implies(falsehood, S9)))), true, is_a_theorem(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y))), true), true), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 201.35/34.01  = { by axiom 3 (c0_CAMeredith) R->L }
% 201.35/34.01    ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Y, falsehood), implies(X, falsehood)), implies(falsehood, S9)), implies(T9, implies(falsehood, S9))), implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y, falsehood), implies(X, falsehood)), implies(falsehood, S9)), implies(T9, implies(falsehood, S9)))), true, is_a_theorem(implies(implies(implies(T9, implies(falsehood, S9)), Y), implies(X, Y))), true), true), true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 201.35/34.01  = { by axiom 2 (condensed_detachment) }
% 201.35/34.01    ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(true, true, is_a_theorem(implies(falsehood, implies(X, Y))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 201.35/34.01  = { by axiom 1 (ifeq_axiom) }
% 201.35/34.01    ifeq(is_a_theorem(implies(implies(falsehood, implies(X, Y)), implies(implies(implies(a, b), a), a))), true, ifeq(is_a_theorem(implies(falsehood, implies(X, Y))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 201.35/34.01  = { by axiom 2 (condensed_detachment) }
% 201.35/34.01    true
% 201.35/34.01  % SZS output end Proof
% 201.35/34.01  
% 201.35/34.01  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------