Twee---2.7.UNS-Prf.s

View TPTP
Problem Process solution in
SystemOnTSTP Download .tgz
%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : LCL086-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n016.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Sep 29 11:49:00 AM UTC 2026

% Result   : Unsatisfiable 0.12s 0.45s
% Output   : Proof 16.76s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : LCL086-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04  % Command  : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35  % Computer : n016.cluster.edu
% 0.09/0.35  % Model    : x86_64 x86_64
% 0.09/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35  % Memory   : 8046.5625MB
% 0.09/0.35  % OS       : Linux 6.8.0-71-generic
% 0.09/0.35  % CPULimit : 300
% 0.09/0.35  % WCLimit  : 300
% 0.09/0.35  % DateTime : Sun Sep 27 15:26:02 UTC 2026
% 0.09/0.35  % CPUTime  : 
% 0.09/0.35  Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.45  Command-line arguments: --no-flatten-goal
% 0.12/0.45  
% 0.12/0.45  % SZS status Unsatisfiable
% 0.12/0.45  
% 12.50/2.24  % SZS output start Proof
% 12.50/2.24  Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 12.50/2.24  Axiom 2 (condensed_detachment): ifeq(is_a_theorem(implies(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 12.50/2.29  Axiom 3 (ic_JLukasiewicz_4): is_a_theorem(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X))))) = true.
% 12.50/2.29  
% 12.50/2.29  Goal 1 (prove_ic_1): is_a_theorem(implies(a, a)) = true.
% 12.50/2.29  Proof:
% 12.50/2.29    is_a_theorem(implies(a, a))
% 12.50/2.29  = { by axiom 1 (ifeq_axiom) R->L }
% 12.50/2.29    ifeq(true, true, is_a_theorem(implies(a, a)), true)
% 12.50/2.29  = { by axiom 2 (condensed_detachment) R->L }
% 12.50/2.29    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(is_a_theorem(implies(a, implies(a, a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 12.50/2.29  = { by axiom 1 (ifeq_axiom) R->L }
% 12.50/2.29    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(true, true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 12.50/2.29  = { by axiom 2 (condensed_detachment) R->L }
% 12.50/2.29    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 12.50/2.29  = { by axiom 1 (ifeq_axiom) R->L }
% 12.50/2.29    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 12.50/2.29  = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 12.50/2.29    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V, U), implies(T, S)), implies(X2, implies(implies(S, V), implies(T, V))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 12.50/2.29  = { by axiom 1 (ifeq_axiom) R->L }
% 12.50/2.29    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V, U), implies(T, S)), implies(X2, implies(implies(S, V), implies(T, V))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 12.50/2.30  = { by axiom 2 (condensed_detachment) R->L }
% 12.50/2.30    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, a)), implies(a, implies(a, a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(a, a), a), implies(a, a)))), implies(implies(implies(implies(V, U), implies(T, S)), implies(X2, implies(implies(S, V), implies(T, V)))), implies(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a))))))), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, a)), implies(a, implies(a, a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(a, a), a), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(V, U), implies(T, S)), implies(X2, implies(implies(S, V), implies(T, V)))), implies(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V, U), implies(T, S)), implies(X2, implies(implies(S, V), implies(T, V))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 12.50/2.30  = { by axiom 3 (ic_JLukasiewicz_4) }
% 13.22/2.30    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, a)), implies(a, implies(a, a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(a, a), a), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(V, U), implies(T, S)), implies(X2, implies(implies(S, V), implies(T, V)))), implies(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V, U), implies(T, S)), implies(X2, implies(implies(S, V), implies(T, V))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.30  = { by axiom 1 (ifeq_axiom) }
% 13.22/2.30    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(a, a)), implies(a, implies(a, a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(a, a), a), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(V, U), implies(T, S)), implies(X2, implies(implies(S, V), implies(T, V)))), implies(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V, U), implies(T, S)), implies(X2, implies(implies(S, V), implies(T, V))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.30  = { by axiom 3 (ic_JLukasiewicz_4) }
% 13.22/2.30    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V, U), implies(T, S)), implies(X2, implies(implies(S, V), implies(T, V)))), implies(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V, U), implies(T, S)), implies(X2, implies(implies(S, V), implies(T, V))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.30  = { by axiom 1 (ifeq_axiom) }
% 13.22/2.30    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V, U), implies(T, S)), implies(X2, implies(implies(S, V), implies(T, V)))), implies(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(V, U), implies(T, S)), implies(X2, implies(implies(S, V), implies(T, V))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.30  = { by axiom 2 (condensed_detachment) }
% 13.22/2.30    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.30  = { by axiom 1 (ifeq_axiom) }
% 13.22/2.30    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.30  = { by axiom 1 (ifeq_axiom) R->L }
% 13.22/2.30    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.30  = { by axiom 2 (condensed_detachment) R->L }
% 13.22/2.30    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))), implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), true, is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.30  = { by axiom 3 (ic_JLukasiewicz_4) }
% 13.22/2.30    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), true, is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.31  = { by axiom 1 (ifeq_axiom) }
% 13.22/2.31    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), true, is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.31  = { by axiom 1 (ifeq_axiom) R->L }
% 13.22/2.31    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), true), true, is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.31  = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 13.22/2.31    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2))))), true, is_a_theorem(implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), true), true, is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.31  = { by axiom 1 (ifeq_axiom) R->L }
% 13.22/2.31    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2))))), true, is_a_theorem(implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.31  = { by axiom 2 (condensed_detachment) R->L }
% 13.22/2.31    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true, is_a_theorem(implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2))))), true, is_a_theorem(implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.31  = { by axiom 1 (ifeq_axiom) R->L }
% 13.22/2.31    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true, is_a_theorem(implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2))))), true, is_a_theorem(implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.31  = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 13.22/2.32    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y3, Z3), implies(W3, V3)), implies(U3, implies(implies(V3, Y3), implies(W3, Y3))))), true, is_a_theorem(implies(implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true, is_a_theorem(implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2))))), true, is_a_theorem(implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.32  = { by axiom 1 (ifeq_axiom) R->L }
% 13.22/2.32    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y3, Z3), implies(W3, V3)), implies(U3, implies(implies(V3, Y3), implies(W3, Y3))))), true, is_a_theorem(implies(implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true, is_a_theorem(implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2))))), true, is_a_theorem(implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.32  = { by axiom 2 (condensed_detachment) R->L }
% 13.22/2.32    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))), implies(a, implies(X3, a))), implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))))), implies(implies(implies(implies(Y3, Z3), implies(W3, V3)), implies(U3, implies(implies(V3, Y3), implies(W3, Y3)))), implies(implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))), implies(a, implies(X3, a))), implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a)))))), true, is_a_theorem(implies(implies(implies(implies(Y3, Z3), implies(W3, V3)), implies(U3, implies(implies(V3, Y3), implies(W3, Y3)))), implies(implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y3, Z3), implies(W3, V3)), implies(U3, implies(implies(V3, Y3), implies(W3, Y3))))), true, is_a_theorem(implies(implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true, is_a_theorem(implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2))))), true, is_a_theorem(implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.32  = { by axiom 3 (ic_JLukasiewicz_4) }
% 13.22/2.32    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))), implies(a, implies(X3, a))), implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a)))))), true, is_a_theorem(implies(implies(implies(implies(Y3, Z3), implies(W3, V3)), implies(U3, implies(implies(V3, Y3), implies(W3, Y3)))), implies(implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y3, Z3), implies(W3, V3)), implies(U3, implies(implies(V3, Y3), implies(W3, Y3))))), true, is_a_theorem(implies(implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true, is_a_theorem(implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2))))), true, is_a_theorem(implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.32  = { by axiom 1 (ifeq_axiom) }
% 13.22/2.33    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))), implies(a, implies(X3, a))), implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a)))))), true, is_a_theorem(implies(implies(implies(implies(Y3, Z3), implies(W3, V3)), implies(U3, implies(implies(V3, Y3), implies(W3, Y3)))), implies(implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y3, Z3), implies(W3, V3)), implies(U3, implies(implies(V3, Y3), implies(W3, Y3))))), true, is_a_theorem(implies(implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true, is_a_theorem(implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2))))), true, is_a_theorem(implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.33  = { by axiom 3 (ic_JLukasiewicz_4) }
% 13.22/2.33    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y3, Z3), implies(W3, V3)), implies(U3, implies(implies(V3, Y3), implies(W3, Y3)))), implies(implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y3, Z3), implies(W3, V3)), implies(U3, implies(implies(V3, Y3), implies(W3, Y3))))), true, is_a_theorem(implies(implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true, is_a_theorem(implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2))))), true, is_a_theorem(implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.33  = { by axiom 1 (ifeq_axiom) }
% 13.22/2.33    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y3, Z3), implies(W3, V3)), implies(U3, implies(implies(V3, Y3), implies(W3, Y3)))), implies(implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))))), true, ifeq(is_a_theorem(implies(implies(implies(Y3, Z3), implies(W3, V3)), implies(U3, implies(implies(V3, Y3), implies(W3, Y3))))), true, is_a_theorem(implies(implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true, is_a_theorem(implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2))))), true, is_a_theorem(implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.33  = { by axiom 2 (condensed_detachment) }
% 13.22/2.33    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true, is_a_theorem(implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2))))), true, is_a_theorem(implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.33  = { by axiom 1 (ifeq_axiom) }
% 13.22/2.33    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true, is_a_theorem(implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2))))), true, is_a_theorem(implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.33  = { by axiom 1 (ifeq_axiom) R->L }
% 13.22/2.33    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true), true, is_a_theorem(implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2))))), true, is_a_theorem(implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.34  = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 13.22/2.34    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3))))), true, is_a_theorem(implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true), true, is_a_theorem(implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2))))), true, is_a_theorem(implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.34  = { by axiom 1 (ifeq_axiom) R->L }
% 13.22/2.34    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3))))), true, is_a_theorem(implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2))))), true, is_a_theorem(implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.34  = { by axiom 2 (condensed_detachment) R->L }
% 13.22/2.34    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(a, a), a)), implies(implies(a, a), X3)), implies(implies(implies(a, a), a), implies(implies(X3, a), implies(implies(a, a), a)))), implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))))), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, a), a)), implies(implies(a, a), X3)), implies(implies(implies(a, a), a), implies(implies(X3, a), implies(implies(a, a), a))))), true, is_a_theorem(implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3))))), true, is_a_theorem(implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2))))), true, is_a_theorem(implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.34  = { by axiom 3 (ic_JLukasiewicz_4) }
% 13.22/2.34    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, a), a)), implies(implies(a, a), X3)), implies(implies(implies(a, a), a), implies(implies(X3, a), implies(implies(a, a), a))))), true, is_a_theorem(implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3))))), true, is_a_theorem(implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2))))), true, is_a_theorem(implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.34  = { by axiom 1 (ifeq_axiom) }
% 13.22/2.34    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, a), a)), implies(implies(a, a), X3)), implies(implies(implies(a, a), a), implies(implies(X3, a), implies(implies(a, a), a))))), true, is_a_theorem(implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3))))), true, is_a_theorem(implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2))))), true, is_a_theorem(implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.34  = { by axiom 3 (ic_JLukasiewicz_4) }
% 13.22/2.35    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3))))), true, is_a_theorem(implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2))))), true, is_a_theorem(implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.35  = { by axiom 1 (ifeq_axiom) }
% 13.22/2.35    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))))), true, ifeq(is_a_theorem(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3))))), true, is_a_theorem(implies(implies(implies(implies(X3, a), implies(implies(a, a), a)), implies(a, implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2))))), true, is_a_theorem(implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.35  = { by axiom 2 (condensed_detachment) }
% 13.22/2.35    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2))))), true, is_a_theorem(implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.35  = { by axiom 1 (ifeq_axiom) }
% 13.22/2.35    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a))))), true, ifeq(is_a_theorem(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2))))), true, is_a_theorem(implies(implies(implies(a, a), a), implies(a, implies(implies(a, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.35  = { by axiom 2 (condensed_detachment) }
% 13.22/2.35    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.35  = { by axiom 1 (ifeq_axiom) }
% 13.22/2.35    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.35  = { by axiom 1 (ifeq_axiom) R->L }
% 13.22/2.35    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.35  = { by axiom 2 (condensed_detachment) R->L }
% 13.22/2.35    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4))))), true, is_a_theorem(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.35  = { by axiom 1 (ifeq_axiom) R->L }
% 13.22/2.35    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4))))), true, is_a_theorem(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.35  = { by axiom 2 (condensed_detachment) R->L }
% 13.22/2.36    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(V5, implies(implies(W5, X5), implies(Z5, X5)))), implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))))), true, ifeq(is_a_theorem(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(V5, implies(implies(W5, X5), implies(Z5, X5))))), true, is_a_theorem(implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4))))), true, is_a_theorem(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.36  = { by axiom 1 (ifeq_axiom) R->L }
% 13.22/2.36    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(V5, implies(implies(W5, X5), implies(Z5, X5)))), implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(V5, implies(implies(W5, X5), implies(Z5, X5))))), true, is_a_theorem(implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4))))), true, is_a_theorem(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.36  = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 13.22/2.36    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z2, implies(Y2, Z2)), implies(Y2, U5)), implies(implies(Y2, Z2), implies(implies(U5, Z2), implies(Y2, Z2))))), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(V5, implies(implies(W5, X5), implies(Z5, X5)))), implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(V5, implies(implies(W5, X5), implies(Z5, X5))))), true, is_a_theorem(implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4))))), true, is_a_theorem(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.36  = { by axiom 1 (ifeq_axiom) R->L }
% 13.22/2.36    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Z2, implies(Y2, Z2)), implies(Y2, U5)), implies(implies(Y2, Z2), implies(implies(U5, Z2), implies(Y2, Z2))))), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(V5, implies(implies(W5, X5), implies(Z5, X5)))), implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(V5, implies(implies(W5, X5), implies(Z5, X5))))), true, is_a_theorem(implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4))))), true, is_a_theorem(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.36  = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 13.22/2.36    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z2, implies(Y2, Z2)), implies(Y2, U5)), implies(implies(Y2, Z2), implies(implies(U5, Z2), implies(Y2, Z2)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(V5, implies(implies(W5, X5), implies(Z5, X5)))), implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))))), true, ifeq(is_a_theorem(implies(implies(implies(Z2, implies(Y2, Z2)), implies(Y2, U5)), implies(implies(Y2, Z2), implies(implies(U5, Z2), implies(Y2, Z2))))), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(V5, implies(implies(W5, X5), implies(Z5, X5)))), implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(V5, implies(implies(W5, X5), implies(Z5, X5))))), true, is_a_theorem(implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4))))), true, is_a_theorem(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.36  = { by axiom 2 (condensed_detachment) }
% 13.22/2.36    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(V5, implies(implies(W5, X5), implies(Z5, X5))))), true, is_a_theorem(implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4))))), true, is_a_theorem(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.36  = { by axiom 1 (ifeq_axiom) }
% 13.22/2.37    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(V5, implies(implies(W5, X5), implies(Z5, X5))))), true, is_a_theorem(implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true), true, is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4))))), true, is_a_theorem(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.37  = { by axiom 3 (ic_JLukasiewicz_4) }
% 13.22/2.37    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true), true, is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4))))), true, is_a_theorem(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.37  = { by axiom 1 (ifeq_axiom) }
% 13.22/2.37    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true, is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4))))), true, is_a_theorem(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.37  = { by axiom 1 (ifeq_axiom) R->L }
% 13.22/2.37    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true, is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4))))), true, is_a_theorem(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.37  = { by axiom 2 (condensed_detachment) R->L }
% 13.22/2.37    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))))), true, ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true, is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4))))), true, is_a_theorem(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.37  = { by axiom 1 (ifeq_axiom) R->L }
% 13.22/2.38    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true, is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4))))), true, is_a_theorem(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.38  = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 13.22/2.38    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(Z2, implies(U5, Z2))), implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2)))))), true, is_a_theorem(implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true, is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4))))), true, is_a_theorem(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.38  = { by axiom 1 (ifeq_axiom) R->L }
% 13.22/2.38    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(Z2, implies(U5, Z2))), implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2)))))), true, is_a_theorem(implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true, is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4))))), true, is_a_theorem(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.38  = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 13.22/2.38    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(Z2, implies(U5, Z2))), implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))))), implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(Z2, implies(U5, Z2))), implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2)))))), true, is_a_theorem(implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true, is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4))))), true, is_a_theorem(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.38  = { by axiom 2 (condensed_detachment) }
% 13.22/2.39    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true, is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4))))), true, is_a_theorem(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.39  = { by axiom 1 (ifeq_axiom) }
% 13.22/2.39    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true, is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4))))), true, is_a_theorem(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.39  = { by axiom 3 (ic_JLukasiewicz_4) }
% 13.22/2.39    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true, is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4))))), true, is_a_theorem(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.39  = { by axiom 1 (ifeq_axiom) }
% 13.22/2.39    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(U5, Z2), implies(Y2, Z2)), implies(Z2, implies(Y2, Z2))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true, is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4))))), true, is_a_theorem(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.39  = { by axiom 2 (condensed_detachment) }
% 13.22/2.39    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4))))), true, is_a_theorem(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.39  = { by axiom 1 (ifeq_axiom) }
% 13.22/2.39    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4))))), true, is_a_theorem(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.39  = { by axiom 3 (ic_JLukasiewicz_4) }
% 13.22/2.39    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.39  = { by axiom 1 (ifeq_axiom) }
% 13.22/2.39    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a))))), true, ifeq(is_a_theorem(implies(implies(Y2, Z2), implies(Z2, implies(Y2, Z2)))), true, is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(a, implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.39  = { by axiom 2 (condensed_detachment) }
% 13.22/2.39    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.39  = { by axiom 1 (ifeq_axiom) }
% 13.22/2.39    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true, is_a_theorem(implies(a, implies(a, a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.39  = { by axiom 1 (ifeq_axiom) R->L }
% 13.22/2.39    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true, ifeq(true, true, is_a_theorem(implies(a, implies(a, a))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.40  = { by axiom 2 (condensed_detachment) R->L }
% 13.22/2.40    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(a, implies(a, a))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.40  = { by axiom 1 (ifeq_axiom) R->L }
% 13.22/2.40    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(a, implies(a, a))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.22/2.40  = { by axiom 2 (condensed_detachment) R->L }
% 13.22/2.40    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(V7, implies(implies(W7, X7), implies(Z7, X7)))), implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))))), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(V7, implies(implies(W7, X7), implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(a, implies(a, a))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.40  = { by axiom 1 (ifeq_axiom) R->L }
% 13.93/2.40    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(V7, implies(implies(W7, X7), implies(Z7, X7)))), implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(V7, implies(implies(W7, X7), implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(a, implies(a, a))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.40  = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 13.93/2.40    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W, implies(Z, W)), implies(Z, U7)), implies(implies(Z, W), implies(implies(U7, W), implies(Z, W))))), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(V7, implies(implies(W7, X7), implies(Z7, X7)))), implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(V7, implies(implies(W7, X7), implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(a, implies(a, a))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.40  = { by axiom 1 (ifeq_axiom) R->L }
% 13.93/2.40    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W, implies(Z, W)), implies(Z, U7)), implies(implies(Z, W), implies(implies(U7, W), implies(Z, W))))), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(V7, implies(implies(W7, X7), implies(Z7, X7)))), implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(V7, implies(implies(W7, X7), implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(a, implies(a, a))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.40  = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 13.93/2.40    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W, implies(Z, W)), implies(Z, U7)), implies(implies(Z, W), implies(implies(U7, W), implies(Z, W)))), implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(V7, implies(implies(W7, X7), implies(Z7, X7)))), implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))))), true, ifeq(is_a_theorem(implies(implies(implies(W, implies(Z, W)), implies(Z, U7)), implies(implies(Z, W), implies(implies(U7, W), implies(Z, W))))), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(V7, implies(implies(W7, X7), implies(Z7, X7)))), implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(V7, implies(implies(W7, X7), implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(a, implies(a, a))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.40  = { by axiom 2 (condensed_detachment) }
% 13.93/2.41    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(V7, implies(implies(W7, X7), implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(a, implies(a, a))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.41  = { by axiom 1 (ifeq_axiom) }
% 13.93/2.41    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(V7, implies(implies(W7, X7), implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(a, implies(a, a))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.41  = { by axiom 3 (ic_JLukasiewicz_4) }
% 13.93/2.41    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(a, implies(a, a))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.41  = { by axiom 1 (ifeq_axiom) }
% 13.93/2.41    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(a, implies(a, a))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.41  = { by axiom 1 (ifeq_axiom) R->L }
% 13.93/2.41    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(a, implies(a, a))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.41  = { by axiom 2 (condensed_detachment) R->L }
% 13.93/2.41    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T7, S7), implies(X8, Y8)), implies(Z8, implies(implies(Y8, T7), implies(X8, T7)))), implies(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))))), true, ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(X8, Y8)), implies(Z8, implies(implies(Y8, T7), implies(X8, T7))))), true, is_a_theorem(implies(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(a, implies(a, a))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.41  = { by axiom 1 (ifeq_axiom) R->L }
% 13.93/2.41    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T7, S7), implies(X8, Y8)), implies(Z8, implies(implies(Y8, T7), implies(X8, T7)))), implies(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(X8, Y8)), implies(Z8, implies(implies(Y8, T7), implies(X8, T7))))), true, is_a_theorem(implies(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(a, implies(a, a))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.41  = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 13.93/2.42    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(W, implies(U7, W))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W)))))), true, is_a_theorem(implies(implies(implies(implies(T7, S7), implies(X8, Y8)), implies(Z8, implies(implies(Y8, T7), implies(X8, T7)))), implies(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(X8, Y8)), implies(Z8, implies(implies(Y8, T7), implies(X8, T7))))), true, is_a_theorem(implies(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(a, implies(a, a))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.42  = { by axiom 1 (ifeq_axiom) R->L }
% 13.93/2.42    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(W, implies(U7, W))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W)))))), true, is_a_theorem(implies(implies(implies(implies(T7, S7), implies(X8, Y8)), implies(Z8, implies(implies(Y8, T7), implies(X8, T7)))), implies(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(X8, Y8)), implies(Z8, implies(implies(Y8, T7), implies(X8, T7))))), true, is_a_theorem(implies(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(a, implies(a, a))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.42  = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 13.93/2.42    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(W, implies(U7, W))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))))), implies(implies(implies(implies(T7, S7), implies(X8, Y8)), implies(Z8, implies(implies(Y8, T7), implies(X8, T7)))), implies(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(W, implies(U7, W))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W)))))), true, is_a_theorem(implies(implies(implies(implies(T7, S7), implies(X8, Y8)), implies(Z8, implies(implies(Y8, T7), implies(X8, T7)))), implies(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(X8, Y8)), implies(Z8, implies(implies(Y8, T7), implies(X8, T7))))), true, is_a_theorem(implies(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(a, implies(a, a))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.42  = { by axiom 2 (condensed_detachment) }
% 13.93/2.42    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(X8, Y8)), implies(Z8, implies(implies(Y8, T7), implies(X8, T7))))), true, is_a_theorem(implies(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(a, implies(a, a))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.42  = { by axiom 1 (ifeq_axiom) }
% 13.93/2.42    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(X8, Y8)), implies(Z8, implies(implies(Y8, T7), implies(X8, T7))))), true, is_a_theorem(implies(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(a, implies(a, a))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.42  = { by axiom 3 (ic_JLukasiewicz_4) }
% 13.93/2.42    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(a, implies(a, a))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.42  = { by axiom 1 (ifeq_axiom) }
% 13.93/2.43    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(a, implies(a, a))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.43  = { by axiom 2 (condensed_detachment) }
% 13.93/2.43    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(a, implies(a, a))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.43  = { by axiom 1 (ifeq_axiom) }
% 13.93/2.43    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.43  = { by axiom 3 (ic_JLukasiewicz_4) }
% 13.93/2.43    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true, is_a_theorem(implies(a, implies(a, a))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.43  = { by axiom 1 (ifeq_axiom) }
% 13.93/2.43    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(a, implies(a, a)))), true, ifeq(is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true, is_a_theorem(implies(a, implies(a, a))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.43  = { by axiom 2 (condensed_detachment) }
% 13.93/2.43    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.43  = { by axiom 1 (ifeq_axiom) }
% 13.93/2.43    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.43  = { by axiom 1 (ifeq_axiom) R->L }
% 13.93/2.43    ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.43  = { by axiom 2 (condensed_detachment) R->L }
% 13.93/2.43    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.43  = { by axiom 3 (ic_JLukasiewicz_4) }
% 13.93/2.43    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.43  = { by axiom 1 (ifeq_axiom) }
% 13.93/2.43    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.43  = { by axiom 1 (ifeq_axiom) R->L }
% 13.93/2.43    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.43  = { by axiom 2 (condensed_detachment) R->L }
% 13.93/2.43    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))))), true, ifeq(is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.43  = { by axiom 3 (ic_JLukasiewicz_4) }
% 13.93/2.43    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.43  = { by axiom 1 (ifeq_axiom) }
% 13.93/2.43    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.43  = { by axiom 1 (ifeq_axiom) R->L }
% 13.93/2.43    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.44  = { by axiom 2 (condensed_detachment) R->L }
% 13.93/2.44    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.44  = { by axiom 1 (ifeq_axiom) R->L }
% 13.93/2.44    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.44  = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 13.93/2.44    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y9, Z9), implies(W9, V9)), implies(U9, implies(implies(V9, Y9), implies(W9, Y9))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.44  = { by axiom 1 (ifeq_axiom) R->L }
% 13.93/2.44    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y9, Z9), implies(W9, V9)), implies(U9, implies(implies(V9, Y9), implies(W9, Y9))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.45  = { by axiom 2 (condensed_detachment) R->L }
% 13.93/2.46    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), implies(implies(implies(implies(Y9, Z9), implies(W9, V9)), implies(U9, implies(implies(V9, Y9), implies(W9, Y9)))), implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true, is_a_theorem(implies(implies(implies(implies(Y9, Z9), implies(W9, V9)), implies(U9, implies(implies(V9, Y9), implies(W9, Y9)))), implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y9, Z9), implies(W9, V9)), implies(U9, implies(implies(V9, Y9), implies(W9, Y9))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.46  = { by axiom 3 (ic_JLukasiewicz_4) }
% 13.93/2.46    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true, is_a_theorem(implies(implies(implies(implies(Y9, Z9), implies(W9, V9)), implies(U9, implies(implies(V9, Y9), implies(W9, Y9)))), implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y9, Z9), implies(W9, V9)), implies(U9, implies(implies(V9, Y9), implies(W9, Y9))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.46  = { by axiom 1 (ifeq_axiom) }
% 13.93/2.46    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true, is_a_theorem(implies(implies(implies(implies(Y9, Z9), implies(W9, V9)), implies(U9, implies(implies(V9, Y9), implies(W9, Y9)))), implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y9, Z9), implies(W9, V9)), implies(U9, implies(implies(V9, Y9), implies(W9, Y9))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.46  = { by axiom 3 (ic_JLukasiewicz_4) }
% 13.93/2.46    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y9, Z9), implies(W9, V9)), implies(U9, implies(implies(V9, Y9), implies(W9, Y9)))), implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y9, Z9), implies(W9, V9)), implies(U9, implies(implies(V9, Y9), implies(W9, Y9))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.46  = { by axiom 1 (ifeq_axiom) }
% 13.93/2.47    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y9, Z9), implies(W9, V9)), implies(U9, implies(implies(V9, Y9), implies(W9, Y9)))), implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))))), true, ifeq(is_a_theorem(implies(implies(implies(Y9, Z9), implies(W9, V9)), implies(U9, implies(implies(V9, Y9), implies(W9, Y9))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.47  = { by axiom 2 (condensed_detachment) }
% 13.93/2.47    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.47  = { by axiom 1 (ifeq_axiom) }
% 13.93/2.47    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.47  = { by axiom 1 (ifeq_axiom) R->L }
% 13.93/2.47    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.47  = { by axiom 2 (condensed_detachment) R->L }
% 13.93/2.47    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))), implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))), true, is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.47  = { by axiom 3 (ic_JLukasiewicz_4) }
% 13.93/2.48    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))), true, is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.48  = { by axiom 1 (ifeq_axiom) }
% 13.93/2.48    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))), true, is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.48  = { by axiom 1 (ifeq_axiom) R->L }
% 13.93/2.48    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.48  = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 13.93/2.48    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.49  = { by axiom 1 (ifeq_axiom) R->L }
% 13.93/2.49    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.49  = { by axiom 2 (condensed_detachment) R->L }
% 13.93/2.49    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(U10, implies(a, a)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(U10, implies(a, a)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 13.93/2.50  = { by axiom 1 (ifeq_axiom) R->L }
% 14.64/2.50    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(U10, implies(a, a)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U10, implies(a, a)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 14.64/2.50  = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 14.64/2.51    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T10, S10), implies(X11, Y11)), implies(Z11, implies(implies(Y11, T10), implies(X11, T10))))), true, is_a_theorem(implies(implies(implies(implies(implies(U10, implies(a, a)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U10, implies(a, a)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 14.64/2.51  = { by axiom 1 (ifeq_axiom) R->L }
% 14.64/2.51    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T10, S10), implies(X11, Y11)), implies(Z11, implies(implies(Y11, T10), implies(X11, T10))))), true, is_a_theorem(implies(implies(implies(implies(implies(U10, implies(a, a)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U10, implies(a, a)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 14.64/2.52  = { by axiom 2 (condensed_detachment) R->L }
% 14.64/2.52    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))), implies(implies(a, a), implies(U10, implies(a, a)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10)))), implies(implies(implies(U10, implies(a, a)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))), implies(implies(implies(implies(T10, S10), implies(X11, Y11)), implies(Z11, implies(implies(Y11, T10), implies(X11, T10)))), implies(implies(implies(implies(implies(U10, implies(a, a)), 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a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 14.64/2.53  = { by axiom 3 (ic_JLukasiewicz_4) }
% 14.64/2.53    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))), implies(implies(a, a), implies(U10, implies(a, a)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10)))), implies(implies(implies(U10, implies(a, a)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))))), true, is_a_theorem(implies(implies(implies(implies(T10, S10), implies(X11, Y11)), implies(Z11, implies(implies(Y11, T10), implies(X11, T10)))), 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Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 14.64/2.54  = { by axiom 1 (ifeq_axiom) }
% 14.64/2.54    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))), implies(implies(a, a), implies(U10, implies(a, a)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10)))), implies(implies(implies(U10, implies(a, a)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))))), true, is_a_theorem(implies(implies(implies(implies(T10, S10), implies(X11, Y11)), implies(Z11, implies(implies(Y11, T10), implies(X11, T10)))), implies(implies(implies(implies(implies(U10, implies(a, a)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T10, S10), implies(X11, Y11)), implies(Z11, implies(implies(Y11, T10), implies(X11, T10))))), true, 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% 14.64/2.54  = { by axiom 3 (ic_JLukasiewicz_4) }
% 14.64/2.54    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T10, S10), implies(X11, Y11)), implies(Z11, implies(implies(Y11, T10), implies(X11, T10)))), implies(implies(implies(implies(implies(U10, implies(a, a)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), 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% 14.64/2.55  = { by axiom 1 (ifeq_axiom) }
% 14.64/2.55    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T10, S10), implies(X11, Y11)), implies(Z11, implies(implies(Y11, T10), implies(X11, T10)))), implies(implies(implies(implies(implies(U10, implies(a, a)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), 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implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U10, implies(a, a)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, 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a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 14.64/2.55  = { by axiom 2 (condensed_detachment) }
% 14.64/2.55    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(U10, implies(a, a)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 14.64/2.55  = { by axiom 1 (ifeq_axiom) }
% 14.64/2.56    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U10, implies(a, a)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 14.64/2.56  = { by axiom 1 (ifeq_axiom) R->L }
% 14.64/2.56    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U10, implies(a, a)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 14.64/2.56  = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 14.64/2.56    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W11, V11), implies(U11, T11)), implies(S11, implies(implies(T11, W11), implies(U11, W11))))), true, is_a_theorem(implies(implies(implies(implies(U10, implies(a, a)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 14.64/2.57  = { by axiom 1 (ifeq_axiom) R->L }
% 14.64/2.57    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W11, V11), implies(U11, T11)), implies(S11, implies(implies(T11, W11), implies(U11, W11))))), true, is_a_theorem(implies(implies(implies(implies(U10, implies(a, a)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 14.64/2.57  = { by axiom 2 (condensed_detachment) R->L }
% 14.64/2.58    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), U10)), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(U10, implies(a, a)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))), implies(implies(implies(implies(W11, V11), implies(U11, T11)), implies(S11, implies(implies(T11, W11), implies(U11, W11)))), implies(implies(implies(implies(U10, implies(a, a)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), U10)), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(U10, implies(a, a)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))), true, is_a_theorem(implies(implies(implies(implies(W11, V11), implies(U11, T11)), implies(S11, implies(implies(T11, W11), implies(U11, W11)))), implies(implies(implies(implies(U10, implies(a, a)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W11, V11), implies(U11, T11)), implies(S11, implies(implies(T11, W11), implies(U11, W11))))), true, is_a_theorem(implies(implies(implies(implies(U10, implies(a, a)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 14.64/2.58  = { by axiom 3 (ic_JLukasiewicz_4) }
% 14.64/2.58    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), U10)), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(U10, implies(a, a)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))), true, is_a_theorem(implies(implies(implies(implies(W11, V11), implies(U11, T11)), implies(S11, implies(implies(T11, W11), implies(U11, W11)))), implies(implies(implies(implies(U10, implies(a, a)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W11, V11), implies(U11, T11)), implies(S11, implies(implies(T11, W11), implies(U11, W11))))), true, is_a_theorem(implies(implies(implies(implies(U10, implies(a, a)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 14.64/2.58  = { by axiom 1 (ifeq_axiom) }
% 14.64/2.59    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), U10)), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(U10, implies(a, a)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))), true, is_a_theorem(implies(implies(implies(implies(W11, V11), implies(U11, T11)), implies(S11, implies(implies(T11, W11), implies(U11, W11)))), implies(implies(implies(implies(U10, implies(a, a)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W11, V11), implies(U11, T11)), implies(S11, implies(implies(T11, W11), implies(U11, W11))))), true, is_a_theorem(implies(implies(implies(implies(U10, implies(a, a)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 14.64/2.59  = { by axiom 3 (ic_JLukasiewicz_4) }
% 14.64/2.59    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W11, V11), implies(U11, T11)), implies(S11, implies(implies(T11, W11), implies(U11, W11)))), implies(implies(implies(implies(U10, implies(a, a)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W11, V11), implies(U11, T11)), implies(S11, implies(implies(T11, W11), implies(U11, W11))))), true, is_a_theorem(implies(implies(implies(implies(U10, implies(a, a)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 14.64/2.59  = { by axiom 1 (ifeq_axiom) }
% 14.64/2.59    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W11, V11), implies(U11, T11)), implies(S11, implies(implies(T11, W11), implies(U11, W11)))), implies(implies(implies(implies(U10, implies(a, a)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))))), true, ifeq(is_a_theorem(implies(implies(implies(W11, V11), implies(U11, T11)), implies(S11, implies(implies(T11, W11), implies(U11, W11))))), true, is_a_theorem(implies(implies(implies(implies(U10, implies(a, a)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 14.64/2.59  = { by axiom 2 (condensed_detachment) }
% 14.64/2.60    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 14.64/2.60  = { by axiom 1 (ifeq_axiom) }
% 14.64/2.60    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(a, a), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 14.64/2.60  = { by axiom 2 (condensed_detachment) }
% 15.35/2.60    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 15.35/2.60  = { by axiom 1 (ifeq_axiom) }
% 15.35/2.60    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 15.35/2.60  = { by axiom 1 (ifeq_axiom) R->L }
% 15.35/2.60    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 15.35/2.61  = { by axiom 2 (condensed_detachment) R->L }
% 15.35/2.61    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true, ifeq(is_a_theorem(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12))))), true, is_a_theorem(implies(implies(T9, S9), implies(S9, implies(T9, S9)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 15.35/2.61  = { by axiom 1 (ifeq_axiom) R->L }
% 15.35/2.62    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12))))), true, is_a_theorem(implies(implies(T9, S9), implies(S9, implies(T9, S9)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 15.35/2.62  = { by axiom 2 (condensed_detachment) R->L }
% 15.35/2.62    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U12, T12), implies(S12, X13)), implies(Y13, implies(implies(X13, U12), implies(S12, U12)))), implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9)))))), true, ifeq(is_a_theorem(implies(implies(implies(U12, T12), implies(S12, X13)), implies(Y13, implies(implies(X13, U12), implies(S12, U12))))), true, is_a_theorem(implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12))))), true, is_a_theorem(implies(implies(T9, S9), implies(S9, implies(T9, S9)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 15.35/2.62  = { by axiom 1 (ifeq_axiom) R->L }
% 15.35/2.62    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U12, T12), implies(S12, X13)), implies(Y13, implies(implies(X13, U12), implies(S12, U12)))), implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U12, T12), implies(S12, X13)), implies(Y13, implies(implies(X13, U12), implies(S12, U12))))), true, is_a_theorem(implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12))))), true, is_a_theorem(implies(implies(T9, S9), implies(S9, implies(T9, S9)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 15.35/2.63  = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 15.35/2.63    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S9, implies(T9, S9)), implies(T9, Z13)), implies(implies(T9, S9), implies(implies(Z13, S9), implies(T9, S9))))), true, is_a_theorem(implies(implies(implies(implies(U12, T12), implies(S12, X13)), implies(Y13, implies(implies(X13, U12), implies(S12, U12)))), implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U12, T12), implies(S12, X13)), implies(Y13, implies(implies(X13, U12), implies(S12, U12))))), true, is_a_theorem(implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12))))), true, is_a_theorem(implies(implies(T9, S9), implies(S9, implies(T9, S9)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 15.35/2.63  = { by axiom 1 (ifeq_axiom) R->L }
% 15.35/2.63    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(S9, implies(T9, S9)), implies(T9, Z13)), implies(implies(T9, S9), implies(implies(Z13, S9), implies(T9, S9))))), true, is_a_theorem(implies(implies(implies(implies(U12, T12), implies(S12, X13)), implies(Y13, implies(implies(X13, U12), implies(S12, U12)))), implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U12, T12), implies(S12, X13)), implies(Y13, implies(implies(X13, U12), implies(S12, U12))))), true, is_a_theorem(implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12))))), true, is_a_theorem(implies(implies(T9, S9), implies(S9, implies(T9, S9)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 15.35/2.63  = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 15.35/2.63    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S9, implies(T9, S9)), implies(T9, Z13)), implies(implies(T9, S9), implies(implies(Z13, S9), implies(T9, S9)))), implies(implies(implies(implies(U12, T12), implies(S12, X13)), implies(Y13, implies(implies(X13, U12), implies(S12, U12)))), implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))))), true, ifeq(is_a_theorem(implies(implies(implies(S9, implies(T9, S9)), implies(T9, Z13)), implies(implies(T9, S9), implies(implies(Z13, S9), implies(T9, S9))))), true, is_a_theorem(implies(implies(implies(implies(U12, T12), implies(S12, X13)), implies(Y13, implies(implies(X13, U12), implies(S12, U12)))), implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U12, T12), implies(S12, X13)), implies(Y13, implies(implies(X13, U12), implies(S12, U12))))), true, is_a_theorem(implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12))))), true, is_a_theorem(implies(implies(T9, S9), implies(S9, implies(T9, S9)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 15.35/2.64  = { by axiom 2 (condensed_detachment) }
% 15.35/2.64    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U12, T12), implies(S12, X13)), implies(Y13, implies(implies(X13, U12), implies(S12, U12))))), true, is_a_theorem(implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12))))), true, is_a_theorem(implies(implies(T9, S9), implies(S9, implies(T9, S9)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 15.35/2.64  = { by axiom 1 (ifeq_axiom) }
% 15.35/2.64    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U12, T12), implies(S12, X13)), implies(Y13, implies(implies(X13, U12), implies(S12, U12))))), true, is_a_theorem(implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true), true, is_a_theorem(implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12))))), true, is_a_theorem(implies(implies(T9, S9), implies(S9, implies(T9, S9)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 15.35/2.64  = { by axiom 3 (ic_JLukasiewicz_4) }
% 15.35/2.64    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true), true, is_a_theorem(implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12))))), true, is_a_theorem(implies(implies(T9, S9), implies(S9, implies(T9, S9)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 15.35/2.65  = { by axiom 1 (ifeq_axiom) }
% 15.35/2.65    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true, is_a_theorem(implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12))))), true, is_a_theorem(implies(implies(T9, S9), implies(S9, implies(T9, S9)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 15.35/2.65  = { by axiom 1 (ifeq_axiom) R->L }
% 15.35/2.65    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true, is_a_theorem(implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12))))), true, is_a_theorem(implies(implies(T9, S9), implies(S9, implies(T9, S9)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 15.35/2.65  = { by axiom 2 (condensed_detachment) R->L }
% 15.35/2.65    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W13, V13), implies(U13, T13)), implies(S13, implies(implies(T13, W13), implies(U13, W13)))), implies(implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9)))), implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))))), true, ifeq(is_a_theorem(implies(implies(implies(W13, V13), implies(U13, T13)), implies(S13, implies(implies(T13, W13), implies(U13, W13))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9)))), implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(T9, S9), implies(S9, implies(T9, S9)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true, is_a_theorem(implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12))))), true, is_a_theorem(implies(implies(T9, S9), implies(S9, implies(T9, S9)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 15.35/2.66  = { by axiom 1 (ifeq_axiom) R->L }
% 15.35/2.66    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W13, V13), implies(U13, T13)), implies(S13, implies(implies(T13, W13), implies(U13, W13)))), implies(implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9)))), implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W13, V13), implies(U13, T13)), implies(S13, implies(implies(T13, W13), implies(U13, W13))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9)))), implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(T9, S9), implies(S9, implies(T9, S9)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true, is_a_theorem(implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12))))), true, is_a_theorem(implies(implies(T9, S9), implies(S9, implies(T9, S9)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 15.35/2.66  = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 15.35/2.66    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(S9, implies(Z13, S9))), implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9)))))), true, is_a_theorem(implies(implies(implies(implies(W13, V13), implies(U13, T13)), implies(S13, implies(implies(T13, W13), implies(U13, W13)))), implies(implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9)))), implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W13, V13), implies(U13, T13)), implies(S13, implies(implies(T13, W13), implies(U13, W13))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9)))), implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(T9, S9), implies(S9, implies(T9, S9)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true, is_a_theorem(implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12))))), true, is_a_theorem(implies(implies(T9, S9), implies(S9, implies(T9, S9)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 15.35/2.67  = { by axiom 1 (ifeq_axiom) R->L }
% 15.35/2.67    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(S9, implies(Z13, S9))), implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9)))))), true, is_a_theorem(implies(implies(implies(implies(W13, V13), implies(U13, T13)), implies(S13, implies(implies(T13, W13), implies(U13, W13)))), implies(implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9)))), implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W13, V13), implies(U13, T13)), implies(S13, implies(implies(T13, W13), implies(U13, W13))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9)))), implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(T9, S9), implies(S9, implies(T9, S9)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true, is_a_theorem(implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12))))), true, is_a_theorem(implies(implies(T9, S9), implies(S9, implies(T9, S9)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 15.35/2.67  = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 15.35/2.67    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(S9, implies(Z13, S9))), implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))))), implies(implies(implies(implies(W13, V13), implies(U13, T13)), implies(S13, implies(implies(T13, W13), implies(U13, W13)))), implies(implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9)))), implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(T9, S9), implies(S9, implies(T9, S9)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(S9, implies(Z13, S9))), implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9)))))), true, is_a_theorem(implies(implies(implies(implies(W13, V13), implies(U13, T13)), implies(S13, implies(implies(T13, W13), implies(U13, W13)))), implies(implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9)))), implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W13, V13), implies(U13, T13)), implies(S13, implies(implies(T13, W13), implies(U13, W13))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9)))), implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(T9, S9), implies(S9, implies(T9, S9)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true, is_a_theorem(implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12))))), true, is_a_theorem(implies(implies(T9, S9), implies(S9, implies(T9, S9)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 15.35/2.67  = { by axiom 2 (condensed_detachment) }
% 15.35/2.68    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W13, V13), implies(U13, T13)), implies(S13, implies(implies(T13, W13), implies(U13, W13))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9)))), implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(T9, S9), implies(S9, implies(T9, S9)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true, is_a_theorem(implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12))))), true, is_a_theorem(implies(implies(T9, S9), implies(S9, implies(T9, S9)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 15.35/2.68  = { by axiom 1 (ifeq_axiom) }
% 15.35/2.68    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W13, V13), implies(U13, T13)), implies(S13, implies(implies(T13, W13), implies(U13, W13))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9)))), implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(T9, S9), implies(S9, implies(T9, S9)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true, is_a_theorem(implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12))))), true, is_a_theorem(implies(implies(T9, S9), implies(S9, implies(T9, S9)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 15.35/2.68  = { by axiom 3 (ic_JLukasiewicz_4) }
% 15.35/2.68    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9)))), implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(T9, S9), implies(S9, implies(T9, S9)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true, is_a_theorem(implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12))))), true, is_a_theorem(implies(implies(T9, S9), implies(S9, implies(T9, S9)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 15.35/2.68  = { by axiom 1 (ifeq_axiom) }
% 15.35/2.68    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9)))), implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(T9, S9), implies(S9, implies(T9, S9)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z13, S9), implies(T9, S9)), implies(S9, implies(T9, S9))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true, is_a_theorem(implies(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12)))), implies(implies(T9, S9), implies(S9, implies(T9, S9))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12))))), true, is_a_theorem(implies(implies(T9, S9), implies(S9, implies(T9, S9)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 15.35/2.68  = { by axiom 2 (condensed_detachment) }
% 15.35/2.69    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12))))), true, is_a_theorem(implies(implies(T9, S9), implies(S9, implies(T9, S9)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 15.35/2.69  = { by axiom 1 (ifeq_axiom) }
% 15.35/2.69    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(X12, Y12), implies(Z12, W12)), implies(V12, implies(implies(W12, X12), implies(Z12, X12))))), true, is_a_theorem(implies(implies(T9, S9), implies(S9, implies(T9, S9)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 15.35/2.69  = { by axiom 3 (ic_JLukasiewicz_4) }
% 15.35/2.69    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(T9, S9), implies(S9, implies(T9, S9)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 15.35/2.69  = { by axiom 1 (ifeq_axiom) }
% 15.35/2.69    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T9, S9), implies(S9, implies(T9, S9))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))))), true, ifeq(is_a_theorem(implies(implies(T9, S9), implies(S9, implies(T9, S9)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)), implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 15.35/2.69  = { by axiom 2 (condensed_detachment) }
% 15.35/2.69    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 15.35/2.69  = { by axiom 1 (ifeq_axiom) }
% 15.35/2.69    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 15.35/2.69  = { by axiom 1 (ifeq_axiom) R->L }
% 15.35/2.69    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(true, true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 15.35/2.70  = { by axiom 2 (condensed_detachment) R->L }
% 15.35/2.70    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true, ifeq(is_a_theorem(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14))))), true, is_a_theorem(implies(implies(S8, X9), implies(X9, implies(S8, X9)))), true), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 15.35/2.70  = { by axiom 1 (ifeq_axiom) R->L }
% 15.35/2.70    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14))))), true, is_a_theorem(implies(implies(S8, X9), implies(X9, implies(S8, X9)))), true), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.70  = { by axiom 2 (condensed_detachment) R->L }
% 16.06/2.70    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U14, T14), implies(S14, X15)), implies(Y15, implies(implies(X15, U14), implies(S14, U14)))), implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9)))))), true, ifeq(is_a_theorem(implies(implies(implies(U14, T14), implies(S14, X15)), implies(Y15, implies(implies(X15, U14), implies(S14, U14))))), true, is_a_theorem(implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14))))), true, is_a_theorem(implies(implies(S8, X9), implies(X9, implies(S8, X9)))), true), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.70  = { by axiom 1 (ifeq_axiom) R->L }
% 16.06/2.70    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U14, T14), implies(S14, X15)), implies(Y15, implies(implies(X15, U14), implies(S14, U14)))), implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U14, T14), implies(S14, X15)), implies(Y15, implies(implies(X15, U14), implies(S14, U14))))), true, is_a_theorem(implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14))))), true, is_a_theorem(implies(implies(S8, X9), implies(X9, implies(S8, X9)))), true), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.70  = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 16.06/2.70    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X9, implies(S8, X9)), implies(S8, Z15)), implies(implies(S8, X9), implies(implies(Z15, X9), implies(S8, X9))))), true, is_a_theorem(implies(implies(implies(implies(U14, T14), implies(S14, X15)), implies(Y15, implies(implies(X15, U14), implies(S14, U14)))), implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U14, T14), implies(S14, X15)), implies(Y15, implies(implies(X15, U14), implies(S14, U14))))), true, is_a_theorem(implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14))))), true, is_a_theorem(implies(implies(S8, X9), implies(X9, implies(S8, X9)))), true), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.71  = { by axiom 1 (ifeq_axiom) R->L }
% 16.06/2.71    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X9, implies(S8, X9)), implies(S8, Z15)), implies(implies(S8, X9), implies(implies(Z15, X9), implies(S8, X9))))), true, is_a_theorem(implies(implies(implies(implies(U14, T14), implies(S14, X15)), implies(Y15, implies(implies(X15, U14), implies(S14, U14)))), implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U14, T14), implies(S14, X15)), implies(Y15, implies(implies(X15, U14), implies(S14, U14))))), true, is_a_theorem(implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14))))), true, is_a_theorem(implies(implies(S8, X9), implies(X9, implies(S8, X9)))), true), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.71  = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 16.06/2.71    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X9, implies(S8, X9)), implies(S8, Z15)), implies(implies(S8, X9), implies(implies(Z15, X9), implies(S8, X9)))), implies(implies(implies(implies(U14, T14), implies(S14, X15)), implies(Y15, implies(implies(X15, U14), implies(S14, U14)))), implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))))), true, ifeq(is_a_theorem(implies(implies(implies(X9, implies(S8, X9)), implies(S8, Z15)), implies(implies(S8, X9), implies(implies(Z15, X9), implies(S8, X9))))), true, is_a_theorem(implies(implies(implies(implies(U14, T14), implies(S14, X15)), implies(Y15, implies(implies(X15, U14), implies(S14, U14)))), implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U14, T14), implies(S14, X15)), implies(Y15, implies(implies(X15, U14), implies(S14, U14))))), true, is_a_theorem(implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14))))), true, is_a_theorem(implies(implies(S8, X9), implies(X9, implies(S8, X9)))), true), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.71  = { by axiom 2 (condensed_detachment) }
% 16.06/2.71    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U14, T14), implies(S14, X15)), implies(Y15, implies(implies(X15, U14), implies(S14, U14))))), true, is_a_theorem(implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14))))), true, is_a_theorem(implies(implies(S8, X9), implies(X9, implies(S8, X9)))), true), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.71  = { by axiom 1 (ifeq_axiom) }
% 16.06/2.71    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U14, T14), implies(S14, X15)), implies(Y15, implies(implies(X15, U14), implies(S14, U14))))), true, is_a_theorem(implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true), true, is_a_theorem(implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14))))), true, is_a_theorem(implies(implies(S8, X9), implies(X9, implies(S8, X9)))), true), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.71  = { by axiom 3 (ic_JLukasiewicz_4) }
% 16.06/2.71    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true), true, is_a_theorem(implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14))))), true, is_a_theorem(implies(implies(S8, X9), implies(X9, implies(S8, X9)))), true), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.72  = { by axiom 1 (ifeq_axiom) }
% 16.06/2.72    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true, is_a_theorem(implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14))))), true, is_a_theorem(implies(implies(S8, X9), implies(X9, implies(S8, X9)))), true), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.72  = { by axiom 1 (ifeq_axiom) R->L }
% 16.06/2.72    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true, is_a_theorem(implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14))))), true, is_a_theorem(implies(implies(S8, X9), implies(X9, implies(S8, X9)))), true), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.72  = { by axiom 2 (condensed_detachment) R->L }
% 16.06/2.72    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9)))), implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))))), true, ifeq(is_a_theorem(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9)))), implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(S8, X9), implies(X9, implies(S8, X9)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true, is_a_theorem(implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14))))), true, is_a_theorem(implies(implies(S8, X9), implies(X9, implies(S8, X9)))), true), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.72  = { by axiom 1 (ifeq_axiom) R->L }
% 16.06/2.73    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9)))), implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9)))), implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(S8, X9), implies(X9, implies(S8, X9)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true, is_a_theorem(implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14))))), true, is_a_theorem(implies(implies(S8, X9), implies(X9, implies(S8, X9)))), true), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.73  = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 16.06/2.73    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(X9, implies(Z15, X9))), implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9)))))), true, is_a_theorem(implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9)))), implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9)))), implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(S8, X9), implies(X9, implies(S8, X9)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true, is_a_theorem(implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14))))), true, is_a_theorem(implies(implies(S8, X9), implies(X9, implies(S8, X9)))), true), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.73  = { by axiom 1 (ifeq_axiom) R->L }
% 16.06/2.73    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(X9, implies(Z15, X9))), implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9)))))), true, is_a_theorem(implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9)))), implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9)))), implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(S8, X9), implies(X9, implies(S8, X9)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true, is_a_theorem(implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14))))), true, is_a_theorem(implies(implies(S8, X9), implies(X9, implies(S8, X9)))), true), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.73  = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 16.06/2.74    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(X9, implies(Z15, X9))), implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))))), implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9)))), implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(S8, X9), implies(X9, implies(S8, X9)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(X9, implies(Z15, X9))), implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9)))))), true, is_a_theorem(implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9)))), implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9)))), implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(S8, X9), implies(X9, implies(S8, X9)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true, is_a_theorem(implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14))))), true, is_a_theorem(implies(implies(S8, X9), implies(X9, implies(S8, X9)))), true), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.74  = { by axiom 2 (condensed_detachment) }
% 16.06/2.74    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9)))), implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(S8, X9), implies(X9, implies(S8, X9)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true, is_a_theorem(implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14))))), true, is_a_theorem(implies(implies(S8, X9), implies(X9, implies(S8, X9)))), true), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.74  = { by axiom 1 (ifeq_axiom) }
% 16.06/2.74    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9)))), implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(S8, X9), implies(X9, implies(S8, X9)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true, is_a_theorem(implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14))))), true, is_a_theorem(implies(implies(S8, X9), implies(X9, implies(S8, X9)))), true), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.74  = { by axiom 3 (ic_JLukasiewicz_4) }
% 16.06/2.75    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9)))), implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(S8, X9), implies(X9, implies(S8, X9)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true, is_a_theorem(implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14))))), true, is_a_theorem(implies(implies(S8, X9), implies(X9, implies(S8, X9)))), true), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.75  = { by axiom 1 (ifeq_axiom) }
% 16.06/2.75    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9)))), implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(S8, X9), implies(X9, implies(S8, X9)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z15, X9), implies(S8, X9)), implies(X9, implies(S8, X9))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true, is_a_theorem(implies(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14)))), implies(implies(S8, X9), implies(X9, implies(S8, X9))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14))))), true, is_a_theorem(implies(implies(S8, X9), implies(X9, implies(S8, X9)))), true), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.75  = { by axiom 2 (condensed_detachment) }
% 16.06/2.75    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14))))), true, is_a_theorem(implies(implies(S8, X9), implies(X9, implies(S8, X9)))), true), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.75  = { by axiom 1 (ifeq_axiom) }
% 16.06/2.75    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(X14, Y14), implies(Z14, W14)), implies(V14, implies(implies(W14, X14), implies(Z14, X14))))), true, is_a_theorem(implies(implies(S8, X9), implies(X9, implies(S8, X9)))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.75  = { by axiom 3 (ic_JLukasiewicz_4) }
% 16.06/2.75    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(S8, X9), implies(X9, implies(S8, X9)))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.75  = { by axiom 1 (ifeq_axiom) }
% 16.06/2.75    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S8, X9), implies(X9, implies(S8, X9))), implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(is_a_theorem(implies(implies(S8, X9), implies(X9, implies(S8, X9)))), true, is_a_theorem(implies(implies(a, a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.75  = { by axiom 2 (condensed_detachment) }
% 16.06/2.75    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.75  = { by axiom 1 (ifeq_axiom) }
% 16.06/2.75    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.75  = { by axiom 1 (ifeq_axiom) R->L }
% 16.06/2.75    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.75  = { by axiom 2 (condensed_detachment) R->L }
% 16.06/2.75    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true, ifeq(is_a_theorem(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16))))), true, is_a_theorem(implies(implies(U8, T8), implies(T8, implies(U8, T8)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.75  = { by axiom 1 (ifeq_axiom) R->L }
% 16.06/2.76    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16))))), true, is_a_theorem(implies(implies(U8, T8), implies(T8, implies(U8, T8)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.76  = { by axiom 2 (condensed_detachment) R->L }
% 16.06/2.76    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U16, T16), implies(S16, X17)), implies(Y17, implies(implies(X17, U16), implies(S16, U16)))), implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8)))))), true, ifeq(is_a_theorem(implies(implies(implies(U16, T16), implies(S16, X17)), implies(Y17, implies(implies(X17, U16), implies(S16, U16))))), true, is_a_theorem(implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16))))), true, is_a_theorem(implies(implies(U8, T8), implies(T8, implies(U8, T8)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.76  = { by axiom 1 (ifeq_axiom) R->L }
% 16.06/2.76    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U16, T16), implies(S16, X17)), implies(Y17, implies(implies(X17, U16), implies(S16, U16)))), implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U16, T16), implies(S16, X17)), implies(Y17, implies(implies(X17, U16), implies(S16, U16))))), true, is_a_theorem(implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16))))), true, is_a_theorem(implies(implies(U8, T8), implies(T8, implies(U8, T8)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.76  = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 16.06/2.76    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T8, implies(U8, T8)), implies(U8, Z17)), implies(implies(U8, T8), implies(implies(Z17, T8), implies(U8, T8))))), true, is_a_theorem(implies(implies(implies(implies(U16, T16), implies(S16, X17)), implies(Y17, implies(implies(X17, U16), implies(S16, U16)))), implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U16, T16), implies(S16, X17)), implies(Y17, implies(implies(X17, U16), implies(S16, U16))))), true, is_a_theorem(implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16))))), true, is_a_theorem(implies(implies(U8, T8), implies(T8, implies(U8, T8)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.76  = { by axiom 1 (ifeq_axiom) R->L }
% 16.06/2.76    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T8, implies(U8, T8)), implies(U8, Z17)), implies(implies(U8, T8), implies(implies(Z17, T8), implies(U8, T8))))), true, is_a_theorem(implies(implies(implies(implies(U16, T16), implies(S16, X17)), implies(Y17, implies(implies(X17, U16), implies(S16, U16)))), implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U16, T16), implies(S16, X17)), implies(Y17, implies(implies(X17, U16), implies(S16, U16))))), true, is_a_theorem(implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16))))), true, is_a_theorem(implies(implies(U8, T8), implies(T8, implies(U8, T8)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.76  = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 16.06/2.76    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T8, implies(U8, T8)), implies(U8, Z17)), implies(implies(U8, T8), implies(implies(Z17, T8), implies(U8, T8)))), implies(implies(implies(implies(U16, T16), implies(S16, X17)), implies(Y17, implies(implies(X17, U16), implies(S16, U16)))), implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))))), true, ifeq(is_a_theorem(implies(implies(implies(T8, implies(U8, T8)), implies(U8, Z17)), implies(implies(U8, T8), implies(implies(Z17, T8), implies(U8, T8))))), true, is_a_theorem(implies(implies(implies(implies(U16, T16), implies(S16, X17)), implies(Y17, implies(implies(X17, U16), implies(S16, U16)))), implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U16, T16), implies(S16, X17)), implies(Y17, implies(implies(X17, U16), implies(S16, U16))))), true, is_a_theorem(implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16))))), true, is_a_theorem(implies(implies(U8, T8), implies(T8, implies(U8, T8)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.76  = { by axiom 2 (condensed_detachment) }
% 16.06/2.77    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U16, T16), implies(S16, X17)), implies(Y17, implies(implies(X17, U16), implies(S16, U16))))), true, is_a_theorem(implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16))))), true, is_a_theorem(implies(implies(U8, T8), implies(T8, implies(U8, T8)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.77  = { by axiom 1 (ifeq_axiom) }
% 16.06/2.77    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U16, T16), implies(S16, X17)), implies(Y17, implies(implies(X17, U16), implies(S16, U16))))), true, is_a_theorem(implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true), true, is_a_theorem(implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16))))), true, is_a_theorem(implies(implies(U8, T8), implies(T8, implies(U8, T8)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.77  = { by axiom 3 (ic_JLukasiewicz_4) }
% 16.06/2.77    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true), true, is_a_theorem(implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16))))), true, is_a_theorem(implies(implies(U8, T8), implies(T8, implies(U8, T8)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.77  = { by axiom 1 (ifeq_axiom) }
% 16.06/2.77    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true, is_a_theorem(implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16))))), true, is_a_theorem(implies(implies(U8, T8), implies(T8, implies(U8, T8)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.77  = { by axiom 1 (ifeq_axiom) R->L }
% 16.06/2.77    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true, is_a_theorem(implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16))))), true, is_a_theorem(implies(implies(U8, T8), implies(T8, implies(U8, T8)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.77  = { by axiom 2 (condensed_detachment) R->L }
% 16.06/2.77    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8)))), implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))))), true, ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8)))), implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(U8, T8), implies(T8, implies(U8, T8)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true, is_a_theorem(implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16))))), true, is_a_theorem(implies(implies(U8, T8), implies(T8, implies(U8, T8)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.77  = { by axiom 1 (ifeq_axiom) R->L }
% 16.06/2.78    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8)))), implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8)))), implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(U8, T8), implies(T8, implies(U8, T8)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true, is_a_theorem(implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16))))), true, is_a_theorem(implies(implies(U8, T8), implies(T8, implies(U8, T8)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.78  = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 16.06/2.78    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(T8, implies(Z17, T8))), implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8)))))), true, is_a_theorem(implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8)))), implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8)))), implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(U8, T8), implies(T8, implies(U8, T8)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true, is_a_theorem(implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16))))), true, is_a_theorem(implies(implies(U8, T8), implies(T8, implies(U8, T8)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.78  = { by axiom 1 (ifeq_axiom) R->L }
% 16.06/2.78    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(T8, implies(Z17, T8))), implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8)))))), true, is_a_theorem(implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8)))), implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8)))), implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(U8, T8), implies(T8, implies(U8, T8)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true, is_a_theorem(implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16))))), true, is_a_theorem(implies(implies(U8, T8), implies(T8, implies(U8, T8)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.78  = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 16.06/2.78    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(T8, implies(Z17, T8))), implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))))), implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8)))), implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(U8, T8), implies(T8, implies(U8, T8)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(T8, implies(Z17, T8))), implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8)))))), true, is_a_theorem(implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8)))), implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8)))), implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(U8, T8), implies(T8, implies(U8, T8)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true, is_a_theorem(implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16))))), true, is_a_theorem(implies(implies(U8, T8), implies(T8, implies(U8, T8)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.78  = { by axiom 2 (condensed_detachment) }
% 16.06/2.79    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8)))), implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(U8, T8), implies(T8, implies(U8, T8)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true, is_a_theorem(implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16))))), true, is_a_theorem(implies(implies(U8, T8), implies(T8, implies(U8, T8)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.79  = { by axiom 1 (ifeq_axiom) }
% 16.06/2.79    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8)))), implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(U8, T8), implies(T8, implies(U8, T8)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true, is_a_theorem(implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16))))), true, is_a_theorem(implies(implies(U8, T8), implies(T8, implies(U8, T8)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.79  = { by axiom 3 (ic_JLukasiewicz_4) }
% 16.06/2.79    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8)))), implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(U8, T8), implies(T8, implies(U8, T8)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true, is_a_theorem(implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16))))), true, is_a_theorem(implies(implies(U8, T8), implies(T8, implies(U8, T8)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.79  = { by axiom 1 (ifeq_axiom) }
% 16.06/2.79    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8)))), implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(U8, T8), implies(T8, implies(U8, T8)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z17, T8), implies(U8, T8)), implies(T8, implies(U8, T8))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true, is_a_theorem(implies(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16)))), implies(implies(U8, T8), implies(T8, implies(U8, T8))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16))))), true, is_a_theorem(implies(implies(U8, T8), implies(T8, implies(U8, T8)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.79  = { by axiom 2 (condensed_detachment) }
% 16.06/2.79    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16))))), true, is_a_theorem(implies(implies(U8, T8), implies(T8, implies(U8, T8)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.79  = { by axiom 1 (ifeq_axiom) }
% 16.06/2.79    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(X16, Y16), implies(Z16, W16)), implies(V16, implies(implies(W16, X16), implies(Z16, X16))))), true, is_a_theorem(implies(implies(U8, T8), implies(T8, implies(U8, T8)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.79  = { by axiom 3 (ic_JLukasiewicz_4) }
% 16.06/2.79    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(U8, T8), implies(T8, implies(U8, T8)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.79  = { by axiom 1 (ifeq_axiom) }
% 16.06/2.79    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(T8, implies(U8, T8))), implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a)))), true, ifeq(is_a_theorem(implies(implies(U8, T8), implies(T8, implies(U8, T8)))), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), a))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.79  = { by axiom 2 (condensed_detachment) }
% 16.06/2.79    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.79  = { by axiom 1 (ifeq_axiom) }
% 16.06/2.79    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.79  = { by axiom 1 (ifeq_axiom) R->L }
% 16.06/2.79    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(true, true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.79  = { by axiom 2 (condensed_detachment) R->L }
% 16.06/2.79    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true, ifeq(is_a_theorem(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.79  = { by axiom 1 (ifeq_axiom) R->L }
% 16.06/2.79    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.80  = { by axiom 2 (condensed_detachment) R->L }
% 16.06/2.80    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U18, T18), implies(S18, X19)), implies(Y19, implies(implies(X19, U18), implies(S18, U18)))), implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))))), true, ifeq(is_a_theorem(implies(implies(implies(U18, T18), implies(S18, X19)), implies(Y19, implies(implies(X19, U18), implies(S18, U18))))), true, is_a_theorem(implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.80  = { by axiom 1 (ifeq_axiom) R->L }
% 16.06/2.80    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U18, T18), implies(S18, X19)), implies(Y19, implies(implies(X19, U18), implies(S18, U18)))), implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U18, T18), implies(S18, X19)), implies(Y19, implies(implies(X19, U18), implies(S18, U18))))), true, is_a_theorem(implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.80  = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 16.06/2.80    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V8, implies(W8, V8)), implies(W8, Z19)), implies(implies(W8, V8), implies(implies(Z19, V8), implies(W8, V8))))), true, is_a_theorem(implies(implies(implies(implies(U18, T18), implies(S18, X19)), implies(Y19, implies(implies(X19, U18), implies(S18, U18)))), implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U18, T18), implies(S18, X19)), implies(Y19, implies(implies(X19, U18), implies(S18, U18))))), true, is_a_theorem(implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.06/2.80  = { by axiom 1 (ifeq_axiom) R->L }
% 16.76/2.80    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V8, implies(W8, V8)), implies(W8, Z19)), implies(implies(W8, V8), implies(implies(Z19, V8), implies(W8, V8))))), true, is_a_theorem(implies(implies(implies(implies(U18, T18), implies(S18, X19)), implies(Y19, implies(implies(X19, U18), implies(S18, U18)))), implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U18, T18), implies(S18, X19)), implies(Y19, implies(implies(X19, U18), implies(S18, U18))))), true, is_a_theorem(implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.76/2.80  = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 16.76/2.80    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V8, implies(W8, V8)), implies(W8, Z19)), implies(implies(W8, V8), implies(implies(Z19, V8), implies(W8, V8)))), implies(implies(implies(implies(U18, T18), implies(S18, X19)), implies(Y19, implies(implies(X19, U18), implies(S18, U18)))), implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))))), true, ifeq(is_a_theorem(implies(implies(implies(V8, implies(W8, V8)), implies(W8, Z19)), implies(implies(W8, V8), implies(implies(Z19, V8), implies(W8, V8))))), true, is_a_theorem(implies(implies(implies(implies(U18, T18), implies(S18, X19)), implies(Y19, implies(implies(X19, U18), implies(S18, U18)))), implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U18, T18), implies(S18, X19)), implies(Y19, implies(implies(X19, U18), implies(S18, U18))))), true, is_a_theorem(implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.76/2.80  = { by axiom 2 (condensed_detachment) }
% 16.76/2.80    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U18, T18), implies(S18, X19)), implies(Y19, implies(implies(X19, U18), implies(S18, U18))))), true, is_a_theorem(implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.76/2.80  = { by axiom 1 (ifeq_axiom) }
% 16.76/2.80    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U18, T18), implies(S18, X19)), implies(Y19, implies(implies(X19, U18), implies(S18, U18))))), true, is_a_theorem(implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true, is_a_theorem(implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.76/2.80  = { by axiom 3 (ic_JLukasiewicz_4) }
% 16.76/2.80    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true, is_a_theorem(implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.76/2.81  = { by axiom 1 (ifeq_axiom) }
% 16.76/2.81    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true, is_a_theorem(implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.76/2.81  = { by axiom 1 (ifeq_axiom) R->L }
% 16.76/2.81    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true, is_a_theorem(implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.76/2.81  = { by axiom 2 (condensed_detachment) R->L }
% 16.76/2.81    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W19, V19), implies(U19, T19)), implies(S19, implies(implies(T19, W19), implies(U19, W19)))), implies(implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))), implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))))), true, ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(U19, T19)), implies(S19, implies(implies(T19, W19), implies(U19, W19))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))), implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true, is_a_theorem(implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.76/2.81  = { by axiom 1 (ifeq_axiom) R->L }
% 16.76/2.81    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W19, V19), implies(U19, T19)), implies(S19, implies(implies(T19, W19), implies(U19, W19)))), implies(implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))), implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(U19, T19)), implies(S19, implies(implies(T19, W19), implies(U19, W19))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))), implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true, is_a_theorem(implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.76/2.81  = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 16.76/2.81    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(V8, implies(Z19, V8))), implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8)))))), true, is_a_theorem(implies(implies(implies(implies(W19, V19), implies(U19, T19)), implies(S19, implies(implies(T19, W19), implies(U19, W19)))), implies(implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))), implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(U19, T19)), implies(S19, implies(implies(T19, W19), implies(U19, W19))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))), implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true, is_a_theorem(implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.76/2.81  = { by axiom 1 (ifeq_axiom) R->L }
% 16.76/2.82    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(V8, implies(Z19, V8))), implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8)))))), true, is_a_theorem(implies(implies(implies(implies(W19, V19), implies(U19, T19)), implies(S19, implies(implies(T19, W19), implies(U19, W19)))), implies(implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))), implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(U19, T19)), implies(S19, implies(implies(T19, W19), implies(U19, W19))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))), implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true, is_a_theorem(implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.76/2.82  = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 16.76/2.82    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(V8, implies(Z19, V8))), implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))))), implies(implies(implies(implies(W19, V19), implies(U19, T19)), implies(S19, implies(implies(T19, W19), implies(U19, W19)))), implies(implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))), implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(V8, implies(Z19, V8))), implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8)))))), true, is_a_theorem(implies(implies(implies(implies(W19, V19), implies(U19, T19)), implies(S19, implies(implies(T19, W19), implies(U19, W19)))), implies(implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))), implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(U19, T19)), implies(S19, implies(implies(T19, W19), implies(U19, W19))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))), implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true, is_a_theorem(implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.76/2.82  = { by axiom 2 (condensed_detachment) }
% 16.76/2.82    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(U19, T19)), implies(S19, implies(implies(T19, W19), implies(U19, W19))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))), implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true, is_a_theorem(implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.76/2.82  = { by axiom 1 (ifeq_axiom) }
% 16.76/2.82    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(U19, T19)), implies(S19, implies(implies(T19, W19), implies(U19, W19))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))), implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true, is_a_theorem(implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.76/2.82  = { by axiom 3 (ic_JLukasiewicz_4) }
% 16.76/2.82    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))), implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true, is_a_theorem(implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.76/2.82  = { by axiom 1 (ifeq_axiom) }
% 16.76/2.82    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))), implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z19, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true, is_a_theorem(implies(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.76/2.82  = { by axiom 2 (condensed_detachment) }
% 16.76/2.82    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.76/2.82  = { by axiom 1 (ifeq_axiom) }
% 16.76/2.82    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(X18, Y18), implies(Z18, W18)), implies(V18, implies(implies(W18, X18), implies(Z18, X18))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.76/2.82  = { by axiom 3 (ic_JLukasiewicz_4) }
% 16.76/2.82    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.76/2.82  = { by axiom 1 (ifeq_axiom) }
% 16.76/2.82    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))))), true, ifeq(is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true, is_a_theorem(implies(implies(a, implies(a, a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.76/2.82  = { by axiom 2 (condensed_detachment) }
% 16.76/2.82    ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true)
% 16.76/2.82  = { by axiom 1 (ifeq_axiom) }
% 16.76/2.82    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true, is_a_theorem(implies(a, a)), true)
% 16.76/2.82  = { by axiom 1 (ifeq_axiom) R->L }
% 16.76/2.82    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 16.76/2.82  = { by axiom 2 (condensed_detachment) R->L }
% 16.76/2.83    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true, ifeq(is_a_theorem(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 16.76/2.83  = { by axiom 1 (ifeq_axiom) R->L }
% 16.76/2.83    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 16.76/2.83  = { by axiom 2 (condensed_detachment) R->L }
% 16.76/2.83    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U20, T20), implies(S20, X21)), implies(Y21, implies(implies(X21, U20), implies(S20, U20)))), implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true, ifeq(is_a_theorem(implies(implies(implies(U20, T20), implies(S20, X21)), implies(Y21, implies(implies(X21, U20), implies(S20, U20))))), true, is_a_theorem(implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 16.76/2.83  = { by axiom 1 (ifeq_axiom) R->L }
% 16.76/2.83    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U20, T20), implies(S20, X21)), implies(Y21, implies(implies(X21, U20), implies(S20, U20)))), implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U20, T20), implies(S20, X21)), implies(Y21, implies(implies(X21, U20), implies(S20, U20))))), true, is_a_theorem(implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 16.76/2.83  = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 16.76/2.83    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y, implies(X, Y)), implies(X, Z21)), implies(implies(X, Y), implies(implies(Z21, Y), implies(X, Y))))), true, is_a_theorem(implies(implies(implies(implies(U20, T20), implies(S20, X21)), implies(Y21, implies(implies(X21, U20), implies(S20, U20)))), implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U20, T20), implies(S20, X21)), implies(Y21, implies(implies(X21, U20), implies(S20, U20))))), true, is_a_theorem(implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 16.76/2.83  = { by axiom 1 (ifeq_axiom) R->L }
% 16.76/2.83    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y, implies(X, Y)), implies(X, Z21)), implies(implies(X, Y), implies(implies(Z21, Y), implies(X, Y))))), true, is_a_theorem(implies(implies(implies(implies(U20, T20), implies(S20, X21)), implies(Y21, implies(implies(X21, U20), implies(S20, U20)))), implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U20, T20), implies(S20, X21)), implies(Y21, implies(implies(X21, U20), implies(S20, U20))))), true, is_a_theorem(implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 16.76/2.83  = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 16.76/2.83    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y, implies(X, Y)), implies(X, Z21)), implies(implies(X, Y), implies(implies(Z21, Y), implies(X, Y)))), implies(implies(implies(implies(U20, T20), implies(S20, X21)), implies(Y21, implies(implies(X21, U20), implies(S20, U20)))), implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))))), true, ifeq(is_a_theorem(implies(implies(implies(Y, implies(X, Y)), implies(X, Z21)), implies(implies(X, Y), implies(implies(Z21, Y), implies(X, Y))))), true, is_a_theorem(implies(implies(implies(implies(U20, T20), implies(S20, X21)), implies(Y21, implies(implies(X21, U20), implies(S20, U20)))), implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U20, T20), implies(S20, X21)), implies(Y21, implies(implies(X21, U20), implies(S20, U20))))), true, is_a_theorem(implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 16.76/2.83  = { by axiom 2 (condensed_detachment) }
% 16.76/2.83    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U20, T20), implies(S20, X21)), implies(Y21, implies(implies(X21, U20), implies(S20, U20))))), true, is_a_theorem(implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 16.76/2.83  = { by axiom 1 (ifeq_axiom) }
% 16.76/2.83    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U20, T20), implies(S20, X21)), implies(Y21, implies(implies(X21, U20), implies(S20, U20))))), true, is_a_theorem(implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, is_a_theorem(implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 16.76/2.83  = { by axiom 3 (ic_JLukasiewicz_4) }
% 16.76/2.83    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, is_a_theorem(implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 16.76/2.83  = { by axiom 1 (ifeq_axiom) }
% 16.76/2.83    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true, is_a_theorem(implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 16.76/2.83  = { by axiom 1 (ifeq_axiom) R->L }
% 16.76/2.83    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true, is_a_theorem(implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 16.76/2.83  = { by axiom 2 (condensed_detachment) R->L }
% 16.76/2.83    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W21, V21), implies(U21, T21)), implies(S21, implies(implies(T21, W21), implies(U21, W21)))), implies(implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(X, Y), implies(Y, implies(X, Y))))))), true, ifeq(is_a_theorem(implies(implies(implies(W21, V21), implies(U21, T21)), implies(S21, implies(implies(T21, W21), implies(U21, W21))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true, is_a_theorem(implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 16.76/2.83  = { by axiom 1 (ifeq_axiom) R->L }
% 16.76/2.84    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W21, V21), implies(U21, T21)), implies(S21, implies(implies(T21, W21), implies(U21, W21)))), implies(implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(X, Y), implies(Y, implies(X, Y))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W21, V21), implies(U21, T21)), implies(S21, implies(implies(T21, W21), implies(U21, W21))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true, is_a_theorem(implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 16.76/2.84  = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 16.76/2.84    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(Y, implies(Z21, Y))), implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y)))))), true, is_a_theorem(implies(implies(implies(implies(W21, V21), implies(U21, T21)), implies(S21, implies(implies(T21, W21), implies(U21, W21)))), implies(implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(X, Y), implies(Y, implies(X, Y))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W21, V21), implies(U21, T21)), implies(S21, implies(implies(T21, W21), implies(U21, W21))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true, is_a_theorem(implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 16.76/2.84  = { by axiom 1 (ifeq_axiom) R->L }
% 16.76/2.84    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(Y, implies(Z21, Y))), implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y)))))), true, is_a_theorem(implies(implies(implies(implies(W21, V21), implies(U21, T21)), implies(S21, implies(implies(T21, W21), implies(U21, W21)))), implies(implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(X, Y), implies(Y, implies(X, Y))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W21, V21), implies(U21, T21)), implies(S21, implies(implies(T21, W21), implies(U21, W21))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true, is_a_theorem(implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 16.76/2.84  = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 16.76/2.84    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(Y, implies(Z21, Y))), implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))))), implies(implies(implies(implies(W21, V21), implies(U21, T21)), implies(S21, implies(implies(T21, W21), implies(U21, W21)))), implies(implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(X, Y), implies(Y, implies(X, Y)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(Y, implies(Z21, Y))), implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y)))))), true, is_a_theorem(implies(implies(implies(implies(W21, V21), implies(U21, T21)), implies(S21, implies(implies(T21, W21), implies(U21, W21)))), implies(implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(X, Y), implies(Y, implies(X, Y))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W21, V21), implies(U21, T21)), implies(S21, implies(implies(T21, W21), implies(U21, W21))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true, is_a_theorem(implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 16.76/2.84  = { by axiom 2 (condensed_detachment) }
% 16.76/2.84    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W21, V21), implies(U21, T21)), implies(S21, implies(implies(T21, W21), implies(U21, W21))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true, is_a_theorem(implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 16.76/2.84  = { by axiom 1 (ifeq_axiom) }
% 16.76/2.84    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W21, V21), implies(U21, T21)), implies(S21, implies(implies(T21, W21), implies(U21, W21))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true, is_a_theorem(implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 16.76/2.84  = { by axiom 3 (ic_JLukasiewicz_4) }
% 16.76/2.84    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true, is_a_theorem(implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 16.76/2.84  = { by axiom 1 (ifeq_axiom) }
% 16.76/2.84    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z21, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true, is_a_theorem(implies(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 16.76/2.84  = { by axiom 2 (condensed_detachment) }
% 16.76/2.84    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 16.76/2.84  = { by axiom 1 (ifeq_axiom) }
% 16.76/2.84    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(X20, Y20), implies(Z20, W20)), implies(V20, implies(implies(W20, X20), implies(Z20, X20))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true, is_a_theorem(implies(a, a)), true), true)
% 16.76/2.84  = { by axiom 3 (ic_JLukasiewicz_4) }
% 16.76/2.84    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true, is_a_theorem(implies(a, a)), true), true)
% 16.76/2.84  = { by axiom 1 (ifeq_axiom) }
% 16.76/2.84    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, a))), true, ifeq(is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true, is_a_theorem(implies(a, a)), true), true)
% 16.76/2.84  = { by axiom 2 (condensed_detachment) }
% 16.76/2.84    true
% 16.76/2.84  % SZS output end Proof
% 16.76/2.84  
% 16.76/2.84  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------