Twee---2.7.THM-Prf.s

View TPTP
Problem Process solution in
SystemOnTSTP Download .tgz
%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : BOO109+1 : TPTP v9.3.1. Released v3.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n008.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 09:35:47 AM UTC 2026

% Result   : Theorem 6.26s 1.13s
% Output   : Proof 25.36s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : BOO109+1 : TPTP v9.3.1. Released v3.5.0.
% 0.00/0.04  % Command  : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.18  % Computer : n008.cluster.edu
% 0.09/0.18  % Model    : x86_64 x86_64
% 0.09/0.18  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18  % Memory   : 8046.5625MB
% 0.09/0.18  % OS       : Linux 6.8.0-71-generic
% 0.09/0.18  % CPULimit : 300
% 0.09/0.18  % WCLimit  : 300
% 0.09/0.18  % DateTime : Mon Sep 28 21:11:54 UTC 2026
% 0.09/0.18  % CPUTime  : 
% 0.09/0.18  Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.26/1.13  Command-line arguments: --flatten --complete-subsets
% 6.26/1.13  
% 6.26/1.13  % SZS status Theorem
% 6.26/1.13  
% 15.73/2.32  % SZS output start Proof
% 15.73/2.32  Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 15.73/2.32  Axiom 2 (modus_ponens_for_nand): ifeq(p(nand(X, nand(Y, Z))), true, ifeq(p(X), true, p(Z), true), true) = true.
% 15.73/2.37  Axiom 3 (wajsbergs_axiom): p(nand(nand(X, nand(Y, Z)), nand(nand(nand(W, Z), nand(nand(X, W), nand(X, W))), nand(X, nand(X, Y))))) = true.
% 15.73/2.37  
% 15.73/2.37  Goal 1 (tautology): p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))) = true.
% 15.73/2.37  Proof:
% 15.73/2.37    p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))
% 15.73/2.37  = { by axiom 1 (ifeq_axiom) R->L }
% 15.73/2.37    ifeq(true, true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 15.73/2.37  = { by axiom 2 (modus_ponens_for_nand) R->L }
% 15.73/2.37    ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(X, a), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), X), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), X))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))))), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 15.73/2.37  = { by axiom 3 (wajsbergs_axiom) }
% 15.73/2.38    ifeq(ifeq(true, true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 15.73/2.38  = { by axiom 1 (ifeq_axiom) }
% 15.73/2.38    ifeq(ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 15.73/2.38  = { by axiom 1 (ifeq_axiom) R->L }
% 15.73/2.38    ifeq(ifeq(ifeq(true, true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 15.73/2.38  = { by axiom 2 (modus_ponens_for_nand) R->L }
% 15.73/2.38    ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), nand(nand(nand(W, nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)), nand(nand(nand(a, a), W), nand(nand(a, a), W))), nand(nand(a, a), nand(nand(a, a), nand(a, a)))))), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 15.73/2.38  = { by axiom 3 (wajsbergs_axiom) }
% 15.73/2.39    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 15.73/2.39  = { by axiom 1 (ifeq_axiom) }
% 15.73/2.39    ifeq(ifeq(ifeq(ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 15.73/2.39  = { by axiom 1 (ifeq_axiom) R->L }
% 15.73/2.39    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 15.73/2.40  = { by axiom 2 (modus_ponens_for_nand) R->L }
% 15.73/2.40    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)), nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))))), true, ifeq(p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 16.40/2.41  = { by axiom 1 (ifeq_axiom) R->L }
% 16.40/2.41    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)), nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))))), true), true, ifeq(p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 16.40/2.41  = { by axiom 3 (wajsbergs_axiom) R->L }
% 16.40/2.42    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)), nand(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))))))), true, p(nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)), nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))))), true), true, ifeq(p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 16.40/2.42  = { by axiom 1 (ifeq_axiom) R->L }
% 16.40/2.42    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(p(nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)), nand(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))))))), true, p(nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)), nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))))), true), true), true, ifeq(p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 16.40/2.43  = { by axiom 3 (wajsbergs_axiom) R->L }
% 16.40/2.43    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)), nand(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))))), nand(nand(nand(V, nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))))), nand(nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)), V), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)), V))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)), nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))))))), true, ifeq(p(nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)), nand(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))))))), true, p(nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)), nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))))), true), true), true, ifeq(p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 16.40/2.44  = { by axiom 2 (modus_ponens_for_nand) }
% 16.40/2.44    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 16.40/2.45  = { by axiom 1 (ifeq_axiom) }
% 16.40/2.45    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 16.40/2.45  = { by axiom 1 (ifeq_axiom) R->L }
% 16.40/2.45    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 16.40/2.45  = { by axiom 2 (modus_ponens_for_nand) R->L }
% 16.40/2.46    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))), true, ifeq(p(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))), true), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 16.40/2.46  = { by axiom 1 (ifeq_axiom) R->L }
% 16.40/2.46    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))), true, ifeq(ifeq(true, true, p(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))), true), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 16.40/2.47  = { by axiom 2 (modus_ponens_for_nand) R->L }
% 16.40/2.47    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))), true, ifeq(ifeq(ifeq(p(nand(nand(nand(a, nand(Y, Z)), nand(nand(nand(U, Z), nand(nand(a, U), nand(a, U))), nand(a, nand(a, Y)))), nand(nand(nand(T, nand(a, nand(a, Y))), nand(nand(nand(a, nand(Y, Z)), T), nand(nand(a, nand(Y, Z)), T))), nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(nand(U, Z), nand(nand(a, U), nand(a, U)))))))), true, ifeq(p(nand(nand(a, nand(Y, Z)), nand(nand(nand(U, Z), nand(nand(a, U), nand(a, U))), nand(a, nand(a, Y))))), true, p(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(nand(U, Z), nand(nand(a, U), nand(a, U)))))), true), true), true, p(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))), true), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 16.40/2.47  = { by axiom 3 (wajsbergs_axiom) }
% 16.40/2.47    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))), true, ifeq(ifeq(ifeq(true, true, ifeq(p(nand(nand(a, nand(Y, Z)), nand(nand(nand(U, Z), nand(nand(a, U), nand(a, U))), nand(a, nand(a, Y))))), true, p(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(nand(U, Z), nand(nand(a, U), nand(a, U)))))), true), true), true, p(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))), true), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 16.40/2.48  = { by axiom 1 (ifeq_axiom) }
% 16.40/2.48    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))), true, ifeq(ifeq(ifeq(p(nand(nand(a, nand(Y, Z)), nand(nand(nand(U, Z), nand(nand(a, U), nand(a, U))), nand(a, nand(a, Y))))), true, p(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(nand(U, Z), nand(nand(a, U), nand(a, U)))))), true), true, p(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))), true), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 16.40/2.48  = { by axiom 3 (wajsbergs_axiom) }
% 16.40/2.48    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))), true, ifeq(ifeq(ifeq(true, true, p(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(nand(U, Z), nand(nand(a, U), nand(a, U)))))), true), true, p(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))), true), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 16.40/2.49  = { by axiom 1 (ifeq_axiom) }
% 16.40/2.49    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))), true, ifeq(ifeq(p(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(nand(U, Z), nand(nand(a, U), nand(a, U)))))), true, p(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))), true), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 16.40/2.49  = { by axiom 1 (ifeq_axiom) R->L }
% 16.40/2.49    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))), true, ifeq(ifeq(true, true, ifeq(p(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(nand(U, Z), nand(nand(a, U), nand(a, U)))))), true, p(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), true), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))), true), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 16.40/2.49  = { by axiom 3 (wajsbergs_axiom) R->L }
% 16.40/2.49    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))), true, ifeq(ifeq(p(nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(nand(U, Z), nand(nand(a, U), nand(a, U))))), nand(nand(nand(S, nand(nand(U, Z), nand(nand(a, U), nand(a, U)))), nand(nand(nand(a, nand(Y, Z)), S), nand(nand(a, nand(Y, Z)), S))), nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))))), true, ifeq(p(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(nand(U, Z), nand(nand(a, U), nand(a, U)))))), true, p(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), true), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))), true), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 16.40/2.50  = { by axiom 2 (modus_ponens_for_nand) }
% 16.40/2.50    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))), true, ifeq(true, true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))), true), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 16.40/2.51  = { by axiom 1 (ifeq_axiom) }
% 17.16/2.51    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 17.16/2.51  = { by axiom 1 (ifeq_axiom) R->L }
% 17.16/2.51    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 17.16/2.52  = { by axiom 2 (modus_ponens_for_nand) R->L }
% 17.16/2.52    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), nand(nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))))), nand(nand(nand(X2, nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))))), nand(nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), X2), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), X2))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))))))), true, ifeq(p(nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), nand(nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))))))), true, p(nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))))), true), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 17.16/2.52  = { by axiom 3 (wajsbergs_axiom) }
% 17.16/2.53    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(p(nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), nand(nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))))))), true, p(nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))))), true), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 17.16/2.53  = { by axiom 1 (ifeq_axiom) }
% 17.16/2.54    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), nand(nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))))))), true, p(nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 17.16/2.54  = { by axiom 3 (wajsbergs_axiom) }
% 17.16/2.54    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 17.16/2.55  = { by axiom 1 (ifeq_axiom) }
% 17.16/2.55    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))))), true, p(nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 17.16/2.55  = { by axiom 1 (ifeq_axiom) R->L }
% 17.16/2.56    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))))), true, ifeq(true, true, p(nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))), true), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 17.16/2.56  = { by axiom 2 (modus_ponens_for_nand) R->L }
% 17.16/2.56    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))))), true, ifeq(ifeq(p(nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(Y2, nand(Y, Z)), nand(nand(nand(a, nand(Y, Z)), Y2), nand(nand(a, nand(Y, Z)), Y2))))), nand(nand(nand(Z2, nand(nand(Y2, nand(Y, Z)), nand(nand(nand(a, nand(Y, Z)), Y2), nand(nand(a, nand(Y, Z)), Y2)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), Z2), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), Z2))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))))))), true, ifeq(p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(Y2, nand(Y, Z)), nand(nand(nand(a, nand(Y, Z)), Y2), nand(nand(a, nand(Y, Z)), Y2)))))), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))))), true), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))), true), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 17.16/2.57  = { by axiom 3 (wajsbergs_axiom) }
% 17.16/2.57    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))))), true, ifeq(ifeq(true, true, ifeq(p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(Y2, nand(Y, Z)), nand(nand(nand(a, nand(Y, Z)), Y2), nand(nand(a, nand(Y, Z)), Y2)))))), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))))), true), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))), true), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 17.16/2.58  = { by axiom 1 (ifeq_axiom) }
% 17.16/2.58    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))))), true, ifeq(ifeq(p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(Y2, nand(Y, Z)), nand(nand(nand(a, nand(Y, Z)), Y2), nand(nand(a, nand(Y, Z)), Y2)))))), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))), true), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 17.16/2.58  = { by axiom 1 (ifeq_axiom) R->L }
% 17.16/2.59    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))))), true, ifeq(ifeq(ifeq(true, true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(Y2, nand(Y, Z)), nand(nand(nand(a, nand(Y, Z)), Y2), nand(nand(a, nand(Y, Z)), Y2)))))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))), true), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 17.16/2.59  = { by axiom 3 (wajsbergs_axiom) R->L }
% 17.16/2.60    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))))), true, ifeq(ifeq(ifeq(p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(Y2, nand(Y, Z)), nand(nand(nand(a, nand(Y, Z)), Y2), nand(nand(a, nand(Y, Z)), Y2))), nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), a))))), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(Y2, nand(Y, Z)), nand(nand(nand(a, nand(Y, Z)), Y2), nand(nand(a, nand(Y, Z)), Y2)))))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))), true), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 17.16/2.60  = { by axiom 1 (ifeq_axiom) R->L }
% 17.93/2.60    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(Y2, nand(Y, Z)), nand(nand(nand(a, nand(Y, Z)), Y2), nand(nand(a, nand(Y, Z)), Y2))), nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), a))))), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(Y2, nand(Y, Z)), nand(nand(nand(a, nand(Y, Z)), Y2), nand(nand(a, nand(Y, Z)), Y2)))))), true), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))), true), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 17.93/2.61  = { by axiom 3 (wajsbergs_axiom) R->L }
% 17.93/2.61    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))))), true, ifeq(ifeq(ifeq(p(nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(Y2, nand(Y, Z)), nand(nand(nand(a, nand(Y, Z)), Y2), nand(nand(a, nand(Y, Z)), Y2))), nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), a)))), nand(nand(nand(W2, nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), a))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), W2), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), W2))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(Y2, nand(Y, Z)), nand(nand(nand(a, nand(Y, Z)), Y2), nand(nand(a, nand(Y, Z)), Y2)))))))), true, ifeq(p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(Y2, nand(Y, Z)), nand(nand(nand(a, nand(Y, Z)), Y2), nand(nand(a, nand(Y, Z)), Y2))), nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), a))))), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(Y2, nand(Y, Z)), nand(nand(nand(a, nand(Y, Z)), Y2), nand(nand(a, nand(Y, Z)), Y2)))))), true), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))), true), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 17.93/2.62  = { by axiom 2 (modus_ponens_for_nand) }
% 17.93/2.62    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))))), true, ifeq(ifeq(true, true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))), true), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 17.93/2.62  = { by axiom 1 (ifeq_axiom) }
% 17.93/2.63    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))))), nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))))), true, ifeq(p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))))), true, p(nand(nand(nand(a, nand(Y, Z)), nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z)))), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))))), true), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 17.93/2.63  = { by axiom 2 (modus_ponens_for_nand) }
% 17.93/2.63    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))), true), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 17.93/2.64  = { by axiom 1 (ifeq_axiom) }
% 17.93/2.64    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 17.93/2.64  = { by axiom 1 (ifeq_axiom) R->L }
% 17.93/2.65    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true), true), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 17.93/2.65  = { by axiom 3 (wajsbergs_axiom) R->L }
% 17.93/2.65    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z))), nand(nand(nand(V2, nand(Y, Z)), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), V2), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), V2))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))))), true, ifeq(p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(a, nand(Y, Z)))), true, p(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), true), true), true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 17.93/2.65  = { by axiom 2 (modus_ponens_for_nand) }
% 17.93/2.65    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 17.93/2.65  = { by axiom 1 (ifeq_axiom) }
% 17.93/2.65    ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 17.93/2.65  = { by axiom 1 (ifeq_axiom) R->L }
% 17.93/2.65    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 17.93/2.66  = { by axiom 3 (wajsbergs_axiom) R->L }
% 17.93/2.66    ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a))), nand(nand(nand(U2, nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)), nand(nand(nand(a, a), U2), nand(nand(a, a), U2))), nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))))), true, ifeq(p(nand(nand(a, a), nand(nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true, p(nand(nand(a, a), nand(nand(a, a), nand(nand(nand(a, nand(Y, Z)), nand(a, nand(Y, Z))), a)))), true), true), true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 17.93/2.66  = { by axiom 2 (modus_ponens_for_nand) }
% 17.93/2.66    ifeq(ifeq(ifeq(ifeq(true, true, p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 17.93/2.66  = { by axiom 1 (ifeq_axiom) }
% 17.93/2.66    ifeq(ifeq(ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 17.93/2.67  = { by axiom 1 (ifeq_axiom) R->L }
% 17.93/2.67    ifeq(ifeq(ifeq(true, true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 17.93/2.68  = { by axiom 2 (modus_ponens_for_nand) R->L }
% 17.93/2.68    ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))))), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true, p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true), true), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 17.93/2.70  = { by axiom 1 (ifeq_axiom) R->L }
% 17.93/2.70    ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))))), true, ifeq(ifeq(true, true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true, p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true), true), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 18.74/2.72  = { by axiom 2 (modus_ponens_for_nand) R->L }
% 18.74/2.73    ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))))), true, ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true, p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true), true), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 18.74/2.75  = { by axiom 1 (ifeq_axiom) R->L }
% 18.74/2.76    ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))))), true, ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true, ifeq(ifeq(true, true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true, p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true), true), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 18.74/2.77  = { by axiom 2 (modus_ponens_for_nand) R->L }
% 18.74/2.79    ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))))), true, ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true, ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(T2, nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), T2), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), T2))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(b, b))))), nand(nand(nand(S2, nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(b, b)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), S2), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), S2))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(T2, nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), T2), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), T2)))))))), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(T2, nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), T2), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), T2))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(b, b)))))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(T2, nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), T2), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), T2)))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true, p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true), true), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 19.53/2.81  = { by axiom 3 (wajsbergs_axiom) }
% 19.53/2.82    ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))))), true, ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(T2, nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), T2), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), T2))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(b, b)))))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(T2, nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), T2), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), T2)))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true, p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true), true), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 19.53/2.84  = { by axiom 1 (ifeq_axiom) }
% 19.53/2.85    ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))))), true, ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true, ifeq(ifeq(ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(T2, nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), T2), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), T2))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(b, b)))))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(T2, nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), T2), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), T2)))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true, p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true), true), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 19.53/2.86  = { by axiom 3 (wajsbergs_axiom) }
% 19.53/2.88    ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))))), true, ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true, ifeq(ifeq(ifeq(true, true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(T2, nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), T2), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), T2)))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true, p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true), true), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 19.53/2.89  = { by axiom 1 (ifeq_axiom) }
% 20.28/2.90    ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))))), true, ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true, ifeq(ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(T2, nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), T2), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), T2)))))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true, p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true), true), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 20.28/2.92  = { by axiom 1 (ifeq_axiom) R->L }
% 20.28/2.93    ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))))), true, ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true, ifeq(ifeq(true, true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(T2, nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), T2), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), T2)))))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true, p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true), true), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 20.28/2.94  = { by axiom 3 (wajsbergs_axiom) R->L }
% 20.28/2.95    ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))))), true, ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true, ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(T2, nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), T2), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), T2))))), nand(nand(nand(X3, nand(nand(T2, nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), T2), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), T2)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), X3), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), X3))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(T2, nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), T2), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), T2)))))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true, p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true), true), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 20.28/2.96  = { by axiom 2 (modus_ponens_for_nand) }
% 20.28/2.97    ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))))), true, ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true, ifeq(true, true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true, p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true), true), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 20.28/2.99  = { by axiom 1 (ifeq_axiom) }
% 20.28/2.99    ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))))), true, ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true, p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true), true), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 20.28/3.01  = { by axiom 1 (ifeq_axiom) R->L }
% 20.28/3.02    ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true, p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true), true), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 20.28/3.03  = { by axiom 3 (wajsbergs_axiom) R->L }
% 20.28/3.04    ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))))), true, ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true, p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true), true), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 20.28/3.04  = { by axiom 1 (ifeq_axiom) R->L }
% 20.28/3.05    ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true, p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true), true), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 20.28/3.05  = { by axiom 3 (wajsbergs_axiom) R->L }
% 21.78/3.06    ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))))), true, ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), nand(nand(nand(Y3, nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), nand(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), Y3), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), Y3))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))))), true, ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true, p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true), true), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 21.78/3.07  = { by axiom 2 (modus_ponens_for_nand) }
% 21.78/3.07    ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))))), true, ifeq(ifeq(ifeq(true, true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true, p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true), true), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 21.78/3.08  = { by axiom 1 (ifeq_axiom) }
% 21.78/3.08    ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))))), true, ifeq(ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true, p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true), true), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 21.78/3.08  = { by axiom 1 (ifeq_axiom) R->L }
% 21.78/3.08    ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))))), true, ifeq(ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true, ifeq(true, true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true), true, p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true), true), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 21.78/3.09  = { by axiom 2 (modus_ponens_for_nand) R->L }
% 21.78/3.10    ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))))), true, ifeq(ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true, ifeq(ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(Z3, nand(a, a)), nand(nand(nand(b, b), Z3), nand(nand(b, b), Z3))))), nand(nand(nand(W3, nand(nand(Z3, nand(a, a)), nand(nand(nand(b, b), Z3), nand(nand(b, b), Z3)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), W3), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), W3))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true, ifeq(p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(Z3, nand(a, a)), nand(nand(nand(b, b), Z3), nand(nand(b, b), Z3)))))), true, p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true), true, p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true), true), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 21.78/3.10  = { by axiom 3 (wajsbergs_axiom) }
% 21.78/3.10    ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))))), true, ifeq(ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true, ifeq(ifeq(true, true, ifeq(p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(Z3, nand(a, a)), nand(nand(nand(b, b), Z3), nand(nand(b, b), Z3)))))), true, p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true), true, p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true), true), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 21.78/3.11  = { by axiom 1 (ifeq_axiom) }
% 21.78/3.11    ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))))), true, ifeq(ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true, ifeq(ifeq(p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(Z3, nand(a, a)), nand(nand(nand(b, b), Z3), nand(nand(b, b), Z3)))))), true, p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true), true, p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true), true), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 21.78/3.11  = { by axiom 1 (ifeq_axiom) R->L }
% 21.78/3.12    ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))))), true, ifeq(ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true, ifeq(ifeq(ifeq(true, true, p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(Z3, nand(a, a)), nand(nand(nand(b, b), Z3), nand(nand(b, b), Z3)))))), true), true, p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true), true, p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true), true), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 21.78/3.12  = { by axiom 3 (wajsbergs_axiom) R->L }
% 21.78/3.13    ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))))), true, ifeq(ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true, ifeq(ifeq(ifeq(p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(Z3, nand(a, a)), nand(nand(nand(b, b), Z3), nand(nand(b, b), Z3))), nand(nand(b, b), nand(nand(b, b), nand(a, a)))))), true, p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(Z3, nand(a, a)), nand(nand(nand(b, b), Z3), nand(nand(b, b), Z3)))))), true), true, p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true), true, p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true), true), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 21.78/3.13  = { by axiom 1 (ifeq_axiom) R->L }
% 21.78/3.13    ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))))), true, ifeq(ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(Z3, nand(a, a)), nand(nand(nand(b, b), Z3), nand(nand(b, b), Z3))), nand(nand(b, b), nand(nand(b, b), nand(a, a)))))), true, p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(Z3, nand(a, a)), nand(nand(nand(b, b), Z3), nand(nand(b, b), Z3)))))), true), true), true, p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true), true, p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true), true), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 21.78/3.14  = { by axiom 3 (wajsbergs_axiom) R->L }
% 21.78/3.14    ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))))), true, ifeq(ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true, ifeq(ifeq(ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(Z3, nand(a, a)), nand(nand(nand(b, b), Z3), nand(nand(b, b), Z3))), nand(nand(b, b), nand(nand(b, b), nand(a, a))))), nand(nand(nand(V3, nand(nand(b, b), nand(nand(b, b), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), V3), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), V3))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(Z3, nand(a, a)), nand(nand(nand(b, b), Z3), nand(nand(b, b), Z3)))))))), true, ifeq(p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(Z3, nand(a, a)), nand(nand(nand(b, b), Z3), nand(nand(b, b), Z3))), nand(nand(b, b), nand(nand(b, b), nand(a, a)))))), true, p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(Z3, nand(a, a)), nand(nand(nand(b, b), Z3), nand(nand(b, b), Z3)))))), true), true), true, p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true), true, p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true), true), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 21.78/3.14  = { by axiom 2 (modus_ponens_for_nand) }
% 21.78/3.15    ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))))), true, ifeq(ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true, ifeq(ifeq(true, true, p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true), true, p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true), true), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 22.54/3.15  = { by axiom 1 (ifeq_axiom) }
% 22.54/3.15    ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))))), true, ifeq(ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true, ifeq(p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true), true, p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true), true), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 22.54/3.16  = { by axiom 2 (modus_ponens_for_nand) }
% 22.54/3.16    ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))))), true, ifeq(true, true, p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true), true), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 22.54/3.16  = { by axiom 1 (ifeq_axiom) }
% 22.54/3.16    ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))))), true, p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 22.54/3.17  = { by axiom 1 (ifeq_axiom) R->L }
% 22.54/3.17    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))))), true), true, p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 22.54/3.17  = { by axiom 3 (wajsbergs_axiom) R->L }
% 22.54/3.17    ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))))), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))))), true), true, p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 22.54/3.17  = { by axiom 1 (ifeq_axiom) R->L }
% 22.54/3.18    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))))), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))))), true), true), true, p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 22.54/3.18  = { by axiom 3 (wajsbergs_axiom) R->L }
% 22.54/3.18    ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b))))), nand(nand(nand(U3, nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), nand(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), U3), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), U3))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))))))), true, ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))))), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))))), true), true), true, p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 22.54/3.18  = { by axiom 2 (modus_ponens_for_nand) }
% 22.54/3.18    ifeq(ifeq(ifeq(ifeq(true, true, p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 22.54/3.18  = { by axiom 1 (ifeq_axiom) }
% 22.54/3.18    ifeq(ifeq(ifeq(p(nand(nand(nand(a, a), nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))))), true, ifeq(p(nand(nand(a, a), nand(nand(a, a), nand(a, a)))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(a, a))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 22.54/3.18  = { by axiom 2 (modus_ponens_for_nand) }
% 22.54/3.18    ifeq(ifeq(true, true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 22.54/3.19  = { by axiom 1 (ifeq_axiom) }
% 22.54/3.19    ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true)
% 22.54/3.19  = { by axiom 1 (ifeq_axiom) R->L }
% 22.54/3.19    ifeq(true, true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 22.54/3.19  = { by axiom 2 (modus_ponens_for_nand) R->L }
% 22.54/3.19    ifeq(ifeq(p(nand(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), nand(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))))), true, ifeq(p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 22.54/3.20  = { by axiom 1 (ifeq_axiom) R->L }
% 22.54/3.20    ifeq(ifeq(ifeq(true, true, p(nand(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), nand(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))))), true), true, ifeq(p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 22.54/3.20  = { by axiom 3 (wajsbergs_axiom) R->L }
% 22.94/3.20    ifeq(ifeq(ifeq(p(nand(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), nand(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), nand(nand(a, nand(b, b)), nand(nand(a, nand(b, b)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))))), true, p(nand(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), nand(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))))), true), true, ifeq(p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 22.94/3.20  = { by axiom 1 (ifeq_axiom) R->L }
% 22.94/3.21    ifeq(ifeq(ifeq(true, true, ifeq(p(nand(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), nand(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), nand(nand(a, nand(b, b)), nand(nand(a, nand(b, b)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))))), true, p(nand(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), nand(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))))), true), true), true, ifeq(p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 22.94/3.21  = { by axiom 3 (wajsbergs_axiom) R->L }
% 22.94/3.22    ifeq(ifeq(ifeq(p(nand(nand(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), nand(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), nand(nand(a, nand(b, b)), nand(nand(a, nand(b, b)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))))), nand(nand(nand(T3, nand(nand(a, nand(b, b)), nand(nand(a, nand(b, b)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), nand(nand(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), T3), nand(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), T3))), nand(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), nand(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))))))), true, ifeq(p(nand(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), nand(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), nand(nand(a, nand(b, b)), nand(nand(a, nand(b, b)), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))))), true, p(nand(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), nand(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))))), true), true), true, ifeq(p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 22.94/3.22  = { by axiom 2 (modus_ponens_for_nand) }
% 22.94/3.22    ifeq(ifeq(true, true, ifeq(p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 22.94/3.22  = { by axiom 1 (ifeq_axiom) }
% 22.94/3.22    ifeq(ifeq(p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 22.94/3.22  = { by axiom 1 (ifeq_axiom) R->L }
% 22.94/3.23    ifeq(ifeq(ifeq(true, true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 22.94/3.23  = { by axiom 2 (modus_ponens_for_nand) R->L }
% 22.94/3.23    ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(S3, nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), S3), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), S3))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))))), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 22.94/3.23  = { by axiom 3 (wajsbergs_axiom) }
% 22.94/3.23    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 22.94/3.24  = { by axiom 1 (ifeq_axiom) }
% 22.94/3.24    ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 22.94/3.25  = { by axiom 1 (ifeq_axiom) R->L }
% 22.94/3.25    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 22.94/3.26  = { by axiom 2 (modus_ponens_for_nand) R->L }
% 22.94/3.26    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 22.94/3.27  = { by axiom 1 (ifeq_axiom) R->L }
% 22.94/3.27    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true, ifeq(ifeq(true, true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 22.94/3.28  = { by axiom 2 (modus_ponens_for_nand) R->L }
% 22.94/3.29    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true, ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(X4, nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), X4), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), X4))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(b, b))))), nand(nand(nand(Y4, nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(b, b)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), Y4), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), Y4))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(X4, nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), X4), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), X4)))))))), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(X4, nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), X4), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), X4))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(b, b)))))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(X4, nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), X4), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), X4)))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 22.94/3.29  = { by axiom 3 (wajsbergs_axiom) }
% 22.94/3.30    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(X4, nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), X4), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), X4))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(b, b)))))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(X4, nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), X4), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), X4)))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 22.94/3.31  = { by axiom 1 (ifeq_axiom) }
% 23.75/3.31    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true, ifeq(ifeq(ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(X4, nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), X4), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), X4))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(b, b)))))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(X4, nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), X4), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), X4)))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 23.75/3.32  = { by axiom 3 (wajsbergs_axiom) }
% 23.75/3.33    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true, ifeq(ifeq(ifeq(true, true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(X4, nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), X4), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), X4)))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 23.75/3.33  = { by axiom 1 (ifeq_axiom) }
% 23.75/3.34    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true, ifeq(ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(X4, nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), X4), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), X4)))))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 23.75/3.34  = { by axiom 1 (ifeq_axiom) R->L }
% 23.75/3.35    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true, ifeq(ifeq(true, true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(X4, nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), X4), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), X4)))))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 23.75/3.35  = { by axiom 3 (wajsbergs_axiom) R->L }
% 23.75/3.36    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true, ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(X4, nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), X4), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), X4))))), nand(nand(nand(Z4, nand(nand(X4, nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), X4), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), X4)))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), Z4), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), Z4))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(X4, nand(nand(a, a), nand(a, a))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), X4), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), X4)))))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 23.75/3.36  = { by axiom 2 (modus_ponens_for_nand) }
% 23.75/3.37    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true, ifeq(true, true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 23.75/3.37  = { by axiom 1 (ifeq_axiom) }
% 23.75/3.38    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 23.75/3.38  = { by axiom 1 (ifeq_axiom) R->L }
% 23.75/3.39    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 23.75/3.39  = { by axiom 3 (wajsbergs_axiom) R->L }
% 23.75/3.40    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 23.75/3.40  = { by axiom 1 (ifeq_axiom) R->L }
% 24.55/3.41    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 24.55/3.41  = { by axiom 3 (wajsbergs_axiom) R->L }
% 24.55/3.42    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), nand(nand(nand(W4, nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), nand(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), W4), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), W4))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))))), true, ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 24.55/3.43  = { by axiom 2 (modus_ponens_for_nand) }
% 24.55/3.43    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 24.55/3.43  = { by axiom 1 (ifeq_axiom) }
% 24.55/3.44    ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 24.55/3.44  = { by axiom 1 (ifeq_axiom) R->L }
% 24.55/3.44    ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true, ifeq(true, true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 24.55/3.45  = { by axiom 2 (modus_ponens_for_nand) R->L }
% 24.55/3.45    ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true, ifeq(ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(V4, nand(a, a)), nand(nand(nand(b, b), V4), nand(nand(b, b), V4))))), nand(nand(nand(U4, nand(nand(V4, nand(a, a)), nand(nand(nand(b, b), V4), nand(nand(b, b), V4)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), U4), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), U4))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true, ifeq(p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(V4, nand(a, a)), nand(nand(nand(b, b), V4), nand(nand(b, b), V4)))))), true, p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 24.55/3.45  = { by axiom 3 (wajsbergs_axiom) }
% 24.55/3.45    ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true, ifeq(ifeq(true, true, ifeq(p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(V4, nand(a, a)), nand(nand(nand(b, b), V4), nand(nand(b, b), V4)))))), true, p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 24.55/3.46  = { by axiom 1 (ifeq_axiom) }
% 24.55/3.46    ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true, ifeq(ifeq(p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(V4, nand(a, a)), nand(nand(nand(b, b), V4), nand(nand(b, b), V4)))))), true, p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 24.55/3.47  = { by axiom 1 (ifeq_axiom) R->L }
% 24.55/3.47    ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true, ifeq(ifeq(ifeq(true, true, p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(V4, nand(a, a)), nand(nand(nand(b, b), V4), nand(nand(b, b), V4)))))), true), true, p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 24.55/3.47  = { by axiom 3 (wajsbergs_axiom) R->L }
% 24.55/3.47    ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true, ifeq(ifeq(ifeq(p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(V4, nand(a, a)), nand(nand(nand(b, b), V4), nand(nand(b, b), V4))), nand(nand(b, b), nand(nand(b, b), nand(a, a)))))), true, p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(V4, nand(a, a)), nand(nand(nand(b, b), V4), nand(nand(b, b), V4)))))), true), true, p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 24.55/3.48  = { by axiom 1 (ifeq_axiom) R->L }
% 24.55/3.48    ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(V4, nand(a, a)), nand(nand(nand(b, b), V4), nand(nand(b, b), V4))), nand(nand(b, b), nand(nand(b, b), nand(a, a)))))), true, p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(V4, nand(a, a)), nand(nand(nand(b, b), V4), nand(nand(b, b), V4)))))), true), true), true, p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 24.55/3.48  = { by axiom 3 (wajsbergs_axiom) R->L }
% 24.55/3.49    ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true, ifeq(ifeq(ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(V4, nand(a, a)), nand(nand(nand(b, b), V4), nand(nand(b, b), V4))), nand(nand(b, b), nand(nand(b, b), nand(a, a))))), nand(nand(nand(T4, nand(nand(b, b), nand(nand(b, b), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), T4), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), T4))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(V4, nand(a, a)), nand(nand(nand(b, b), V4), nand(nand(b, b), V4)))))))), true, ifeq(p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(V4, nand(a, a)), nand(nand(nand(b, b), V4), nand(nand(b, b), V4))), nand(nand(b, b), nand(nand(b, b), nand(a, a)))))), true, p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(V4, nand(a, a)), nand(nand(nand(b, b), V4), nand(nand(b, b), V4)))))), true), true), true, p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 24.55/3.49  = { by axiom 2 (modus_ponens_for_nand) }
% 24.55/3.49    ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true, ifeq(ifeq(true, true, p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 24.55/3.49  = { by axiom 1 (ifeq_axiom) }
% 24.55/3.49    ifeq(ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), true, ifeq(p(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), true), true), true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 24.55/3.49  = { by axiom 2 (modus_ponens_for_nand) }
% 24.55/3.50    ifeq(ifeq(ifeq(ifeq(true, true, p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 24.55/3.50  = { by axiom 1 (ifeq_axiom) }
% 24.55/3.50    ifeq(ifeq(ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 25.36/3.50  = { by axiom 1 (ifeq_axiom) R->L }
% 25.36/3.50    ifeq(ifeq(ifeq(true, true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 25.36/3.51  = { by axiom 2 (modus_ponens_for_nand) R->L }
% 25.36/3.51    ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b))), nand(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), nand(nand(nand(S4, nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))), nand(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b))), S4), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b))), S4))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b))), nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))))))), true, ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b))), nand(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b))), nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))))), true), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 25.36/3.52  = { by axiom 3 (wajsbergs_axiom) }
% 25.36/3.52    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b))), nand(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b))), nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))))), true), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 25.36/3.52  = { by axiom 1 (ifeq_axiom) }
% 25.36/3.52    ifeq(ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b))), nand(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))))))), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b))), nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 25.36/3.52  = { by axiom 3 (wajsbergs_axiom) }
% 25.36/3.53    ifeq(ifeq(ifeq(ifeq(true, true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b))), nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 25.36/3.53  = { by axiom 1 (ifeq_axiom) }
% 25.36/3.53    ifeq(ifeq(ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b))), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b))), nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))))), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(b, b)))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)))), true), true), true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 25.36/3.53  = { by axiom 2 (modus_ponens_for_nand) }
% 25.36/3.53    ifeq(ifeq(true, true, p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 25.36/3.53  = { by axiom 1 (ifeq_axiom) }
% 25.36/3.53    ifeq(p(nand(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a)), nand(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a))))), nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))))), true, ifeq(p(nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), nand(nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))), a))), true, p(nand(nand(a, nand(b, b)), nand(nand(nand(b, b), nand(nand(a, a), nand(a, a))), nand(nand(b, b), nand(nand(a, a), nand(a, a)))))), true), true)
% 25.36/3.53  = { by axiom 2 (modus_ponens_for_nand) }
% 25.36/3.53    true
% 25.36/3.53  % SZS output end Proof
% 25.36/3.53  
% 25.36/3.53  RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------