Twee---2.7.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : LCL083-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n026.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Sep 29 11:48:59 AM UTC 2026

% Result   : Unsatisfiable 3.45s 1.02s
% Output   : Proof 46.09s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : LCL083-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04  % Command  : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37  % Computer : n026.cluster.edu
% 0.10/0.37  % Model    : x86_64 x86_64
% 0.10/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37  % Memory   : 8046.5625MB
% 0.10/0.37  % OS       : Linux 6.8.0-71-generic
% 0.10/0.37  % CPULimit : 300
% 0.10/0.37  % WCLimit  : 300
% 0.10/0.37  % DateTime : Sun Sep 27 15:23:56 UTC 2026
% 0.10/0.37  % CPUTime  : 
% 0.10/0.37  Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.45/1.02  Command-line arguments: --no-flatten-goal
% 3.45/1.02  
% 3.45/1.02  % SZS status Unsatisfiable
% 3.45/1.02  
% 40.68/10.82  % SZS output start Proof
% 40.68/10.82  Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 40.68/10.82  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.
% 41.09/11.03  Axiom 3 (ic_JLukasiewicz): is_a_theorem(implies(implies(implies(X, Y), Z), implies(implies(Z, X), implies(W, X)))) = true.
% 41.09/11.03  
% 41.09/11.03  Goal 1 (prove_ic_3): is_a_theorem(implies(implies(implies(a, b), a), a)) = true.
% 41.09/11.03  Proof:
% 41.09/11.03    is_a_theorem(implies(implies(implies(a, b), a), a))
% 41.09/11.03  = { by axiom 1 (ifeq_axiom) R->L }
% 41.09/11.03    ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.09/11.04  = { by axiom 2 (condensed_detachment) R->L }
% 41.09/11.04    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.09/11.04  = { by axiom 1 (ifeq_axiom) R->L }
% 41.09/11.04    ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.09/11.04  = { by axiom 2 (condensed_detachment) R->L }
% 41.09/11.04    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, ifeq(is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.09/11.04  = { by axiom 1 (ifeq_axiom) R->L }
% 41.09/11.04    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.09/11.05  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 41.09/11.05    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(V, U), T), implies(implies(T, V), implies(S, V)))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.09/11.05  = { by axiom 1 (ifeq_axiom) R->L }
% 41.09/11.05    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V, U), T), implies(implies(T, V), implies(S, V)))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.09/11.05  = { by axiom 2 (condensed_detachment) R->L }
% 41.09/11.05    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(X2, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))), implies(implies(implies(implies(V, U), T), implies(implies(T, V), implies(S, V))), implies(implies(Z, W), implies(W, implies(Z, W)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(X2, 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(V, U), T), implies(implies(T, V), implies(S, V))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V, U), T), implies(implies(T, V), implies(S, V)))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.09/11.06  = { by axiom 1 (ifeq_axiom) R->L }
% 41.09/11.06    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(X2, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))), implies(implies(implies(implies(V, U), T), implies(implies(T, V), implies(S, V))), implies(implies(Z, W), implies(W, implies(Z, W)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X2, 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(V, U), T), implies(implies(T, V), implies(S, V))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V, U), T), implies(implies(T, V), implies(S, V)))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.09/11.06  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 41.09/11.07    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(X2, W)), implies(implies(implies(X2, W), implies(Z, W)), implies(W, implies(Z, W))))), true, is_a_theorem(implies(implies(implies(implies(implies(X2, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))), implies(implies(implies(implies(V, U), T), implies(implies(T, V), implies(S, V))), implies(implies(Z, W), implies(W, implies(Z, W)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X2, 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(V, U), T), implies(implies(T, V), implies(S, V))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V, U), T), implies(implies(T, V), implies(S, V)))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.09/11.07  = { by axiom 1 (ifeq_axiom) R->L }
% 41.09/11.07    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(X2, W)), implies(implies(implies(X2, W), implies(Z, W)), implies(W, implies(Z, W))))), true, is_a_theorem(implies(implies(implies(implies(implies(X2, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))), implies(implies(implies(implies(V, U), T), implies(implies(T, V), implies(S, V))), implies(implies(Z, W), implies(W, implies(Z, W)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X2, 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(V, U), T), implies(implies(T, V), implies(S, V))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V, U), T), implies(implies(T, V), implies(S, V)))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.09/11.07  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 41.09/11.08    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(X2, W)), implies(implies(implies(X2, W), implies(Z, W)), implies(W, implies(Z, W)))), implies(implies(implies(implies(implies(X2, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))), implies(implies(implies(implies(V, U), T), implies(implies(T, V), implies(S, V))), 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(X2, W)), implies(implies(implies(X2, W), implies(Z, W)), implies(W, implies(Z, W))))), true, is_a_theorem(implies(implies(implies(implies(implies(X2, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))), implies(implies(implies(implies(V, U), T), implies(implies(T, V), implies(S, V))), implies(implies(Z, W), implies(W, implies(Z, W)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X2, 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(V, U), T), implies(implies(T, V), implies(S, V))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V, U), T), implies(implies(T, V), implies(S, V)))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.09/11.08  = { by axiom 2 (condensed_detachment) }
% 41.09/11.08    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(X2, 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(V, U), T), implies(implies(T, V), implies(S, V))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V, U), T), implies(implies(T, V), implies(S, V)))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.09/11.08  = { by axiom 1 (ifeq_axiom) }
% 41.09/11.08    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X2, 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(V, U), T), implies(implies(T, V), implies(S, V))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V, U), T), implies(implies(T, V), implies(S, V)))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.09/11.09  = { by axiom 1 (ifeq_axiom) R->L }
% 41.09/11.09    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X2, 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(V, U), T), implies(implies(T, V), implies(S, V))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V, U), T), implies(implies(T, V), implies(S, V)))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.09/11.09  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 41.09/11.09    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W, implies(Z, W)), X2), implies(implies(X2, W), implies(Z, W)))), true, is_a_theorem(implies(implies(implies(implies(X2, 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(V, U), T), implies(implies(T, V), implies(S, V))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V, U), T), implies(implies(T, V), implies(S, V)))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.09/11.09  = { by axiom 1 (ifeq_axiom) R->L }
% 41.09/11.10    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W, implies(Z, W)), X2), implies(implies(X2, W), implies(Z, W)))), true, is_a_theorem(implies(implies(implies(implies(X2, 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(V, U), T), implies(implies(T, V), implies(S, V))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V, U), T), implies(implies(T, V), implies(S, V)))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.09/11.10  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 41.09/11.10    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W, implies(Z, W)), X2), implies(implies(X2, W), implies(Z, W))), implies(implies(implies(implies(X2, 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)), X2), implies(implies(X2, W), implies(Z, W)))), true, is_a_theorem(implies(implies(implies(implies(X2, 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(V, U), T), implies(implies(T, V), implies(S, V))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V, U), T), implies(implies(T, V), implies(S, V)))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.28/11.10  = { by axiom 2 (condensed_detachment) }
% 41.28/11.10    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V, U), T), implies(implies(T, V), implies(S, V))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V, U), T), implies(implies(T, V), implies(S, V)))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.28/11.10  = { by axiom 1 (ifeq_axiom) }
% 41.28/11.11    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V, U), T), implies(implies(T, V), implies(S, V))), implies(implies(Z, W), implies(W, implies(Z, W))))), true, ifeq(is_a_theorem(implies(implies(implies(V, U), T), implies(implies(T, V), implies(S, V)))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.28/11.11  = { by axiom 2 (condensed_detachment) }
% 41.28/11.11    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.28/11.11  = { by axiom 1 (ifeq_axiom) }
% 41.28/11.11    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.28/11.11  = { by axiom 1 (ifeq_axiom) R->L }
% 41.28/11.11    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.28/11.12  = { by axiom 2 (condensed_detachment) R->L }
% 41.28/11.12    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.28/11.12  = { by axiom 3 (ic_JLukasiewicz) }
% 41.28/11.12    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.28/11.13  = { by axiom 1 (ifeq_axiom) }
% 41.28/11.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.28/11.14  = { by axiom 1 (ifeq_axiom) R->L }
% 41.28/11.14    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.28/11.14  = { by axiom 2 (condensed_detachment) R->L }
% 41.28/11.15    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))), true, is_a_theorem(implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.28/11.15  = { by axiom 3 (ic_JLukasiewicz) }
% 41.28/11.15    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))))), true, ifeq(true, true, is_a_theorem(implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.28/11.16  = { by axiom 1 (ifeq_axiom) }
% 41.28/11.16    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))))), true, is_a_theorem(implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.28/11.17  = { by axiom 1 (ifeq_axiom) R->L }
% 41.28/11.18    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))))), true), true, is_a_theorem(implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.28/11.18  = { by axiom 2 (condensed_detachment) R->L }
% 41.28/11.19    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), U2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))), T2), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), U2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))), T2), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))))), true), true, is_a_theorem(implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.28/11.20  = { by axiom 3 (ic_JLukasiewicz) }
% 41.28/11.20    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), U2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))), T2), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))), T2), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))))), true), true, is_a_theorem(implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.28/11.21  = { by axiom 1 (ifeq_axiom) }
% 41.28/11.22    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), U2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))), T2), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))), T2), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))))), true), true, is_a_theorem(implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.28/11.22  = { by axiom 1 (ifeq_axiom) R->L }
% 41.28/11.23    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), U2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))), T2), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))), T2), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))))), true), true, is_a_theorem(implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.28/11.24  = { by axiom 2 (condensed_detachment) R->L }
% 41.58/11.25    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(a, b), a), U2), implies(implies(implies(a, b), a), a))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(a, b), a), U2), implies(implies(implies(a, b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), U2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))), T2), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))), T2), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))))), true), true, is_a_theorem(implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.58/11.25  = { by axiom 3 (ic_JLukasiewicz) }
% 41.58/11.26    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(a, b), a), U2), implies(implies(implies(a, b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), U2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))), T2), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))), T2), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))))), true), true, is_a_theorem(implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.58/11.27  = { by axiom 1 (ifeq_axiom) }
% 41.58/11.28    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(a, b), a), U2), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), U2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))), T2), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))), T2), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))))), true), true, is_a_theorem(implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.58/11.28  = { by axiom 3 (ic_JLukasiewicz) }
% 41.58/11.29    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(a, b), a), U2), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), U2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))), T2), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))), T2), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))))), true), true, is_a_theorem(implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.58/11.30  = { by axiom 1 (ifeq_axiom) }
% 41.58/11.31    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(a, b), a), U2), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), U2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))), T2), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))), T2), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))))), true), true, is_a_theorem(implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.58/11.31  = { by axiom 1 (ifeq_axiom) R->L }
% 41.58/11.32    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(a, b), a), U2), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), U2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))), T2), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))), T2), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))))), true), true, is_a_theorem(implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.58/11.32  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 41.58/11.33    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(a, b), a), U2), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(implies(a, b), a), U2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))), T2), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(a, b), a), U2), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), U2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))), T2), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))), T2), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))))), true), true, is_a_theorem(implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.58/11.34  = { by axiom 2 (condensed_detachment) }
% 41.58/11.34    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))), T2), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))))), true), true, is_a_theorem(implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.78/11.35  = { by axiom 1 (ifeq_axiom) }
% 41.78/11.35    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))), T2), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))))), true), true, is_a_theorem(implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.78/11.35  = { by axiom 1 (ifeq_axiom) R->L }
% 41.78/11.36    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))), T2), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))))), true), true), true, is_a_theorem(implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.78/11.36  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 41.78/11.37    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))), T2), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))), T2), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))))), true), true), true, is_a_theorem(implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.78/11.38  = { by axiom 2 (condensed_detachment) }
% 41.78/11.38    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.78/11.38  = { by axiom 1 (ifeq_axiom) }
% 41.78/11.38    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.78/11.39  = { by axiom 1 (ifeq_axiom) R->L }
% 41.78/11.39    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.78/11.39  = { by axiom 2 (condensed_detachment) R->L }
% 41.78/11.40    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(S2, V2), implies(W2, V2)), implies(V2, implies(W2, V2))), implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(S2, V2), implies(W2, V2)), implies(V2, implies(W2, V2))), implies(implies(W2, V2), implies(V2, implies(W2, V2))))), true, is_a_theorem(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.91/11.40  = { by axiom 1 (ifeq_axiom) R->L }
% 41.91/11.41    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(S2, V2), implies(W2, V2)), implies(V2, implies(W2, V2))), implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S2, V2), implies(W2, V2)), implies(V2, implies(W2, V2))), implies(implies(W2, V2), implies(V2, implies(W2, V2))))), true, is_a_theorem(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.91/11.41  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 41.91/11.41    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W2, V2), implies(V2, implies(W2, V2))), implies(S2, V2)), implies(implies(implies(S2, V2), implies(W2, V2)), implies(V2, implies(W2, V2))))), true, is_a_theorem(implies(implies(implies(implies(implies(S2, V2), implies(W2, V2)), implies(V2, implies(W2, V2))), implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S2, V2), implies(W2, V2)), implies(V2, implies(W2, V2))), implies(implies(W2, V2), implies(V2, implies(W2, V2))))), true, is_a_theorem(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.91/11.42  = { by axiom 1 (ifeq_axiom) R->L }
% 41.91/11.42    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(W2, V2), implies(V2, implies(W2, V2))), implies(S2, V2)), implies(implies(implies(S2, V2), implies(W2, V2)), implies(V2, implies(W2, V2))))), true, is_a_theorem(implies(implies(implies(implies(implies(S2, V2), implies(W2, V2)), implies(V2, implies(W2, V2))), implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S2, V2), implies(W2, V2)), implies(V2, implies(W2, V2))), implies(implies(W2, V2), implies(V2, implies(W2, V2))))), true, is_a_theorem(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.91/11.42  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 41.91/11.43    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(W2, V2), implies(V2, implies(W2, V2))), implies(S2, V2)), implies(implies(implies(S2, V2), implies(W2, V2)), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(S2, V2), implies(W2, V2)), implies(V2, implies(W2, V2))), implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(W2, V2), implies(V2, implies(W2, V2))), implies(S2, V2)), implies(implies(implies(S2, V2), implies(W2, V2)), implies(V2, implies(W2, V2))))), true, is_a_theorem(implies(implies(implies(implies(implies(S2, V2), implies(W2, V2)), implies(V2, implies(W2, V2))), implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S2, V2), implies(W2, V2)), implies(V2, implies(W2, V2))), implies(implies(W2, V2), implies(V2, implies(W2, V2))))), true, is_a_theorem(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.91/11.43  = { by axiom 2 (condensed_detachment) }
% 41.91/11.43    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(S2, V2), implies(W2, V2)), implies(V2, implies(W2, V2))), implies(implies(W2, V2), implies(V2, implies(W2, V2))))), true, is_a_theorem(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.91/11.44  = { by axiom 1 (ifeq_axiom) }
% 41.91/11.44    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S2, V2), implies(W2, V2)), implies(V2, implies(W2, V2))), implies(implies(W2, V2), implies(V2, implies(W2, V2))))), true, is_a_theorem(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.91/11.44  = { by axiom 1 (ifeq_axiom) R->L }
% 41.91/11.45    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S2, V2), implies(W2, V2)), implies(V2, implies(W2, V2))), implies(implies(W2, V2), implies(V2, implies(W2, V2))))), true), true, is_a_theorem(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.91/11.45  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 41.91/11.45    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V2, implies(W2, V2)), S2), implies(implies(S2, V2), implies(W2, V2)))), true, is_a_theorem(implies(implies(implies(implies(S2, V2), implies(W2, V2)), implies(V2, implies(W2, V2))), implies(implies(W2, V2), implies(V2, implies(W2, V2))))), true), true, is_a_theorem(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.91/11.45  = { by axiom 1 (ifeq_axiom) R->L }
% 41.91/11.46    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V2, implies(W2, V2)), S2), implies(implies(S2, V2), implies(W2, V2)))), true, is_a_theorem(implies(implies(implies(implies(S2, V2), implies(W2, V2)), implies(V2, implies(W2, V2))), implies(implies(W2, V2), implies(V2, implies(W2, V2))))), true), true), true, is_a_theorem(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.91/11.46  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 41.91/11.46    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V2, implies(W2, V2)), S2), implies(implies(S2, V2), implies(W2, V2))), implies(implies(implies(implies(S2, V2), implies(W2, V2)), implies(V2, implies(W2, V2))), implies(implies(W2, V2), implies(V2, implies(W2, V2)))))), true, ifeq(is_a_theorem(implies(implies(implies(V2, implies(W2, V2)), S2), implies(implies(S2, V2), implies(W2, V2)))), true, is_a_theorem(implies(implies(implies(implies(S2, V2), implies(W2, V2)), implies(V2, implies(W2, V2))), implies(implies(W2, V2), implies(V2, implies(W2, V2))))), true), true), true, is_a_theorem(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.91/11.46  = { by axiom 2 (condensed_detachment) }
% 41.91/11.47    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.91/11.47  = { by axiom 1 (ifeq_axiom) }
% 41.91/11.47    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a))))), true, ifeq(is_a_theorem(implies(Z2, implies(implies(W2, V2), implies(V2, implies(W2, V2))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(a, b), a), a)), implies(implies(a, Y2), implies(implies(implies(a, b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.91/11.47  = { by axiom 2 (condensed_detachment) }
% 41.91/11.47    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.91/11.48  = { by axiom 1 (ifeq_axiom) }
% 41.91/11.48    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.91/11.48  = { by axiom 1 (ifeq_axiom) R->L }
% 41.91/11.48    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.91/11.48  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 41.91/11.48    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))))), true, ifeq(is_a_theorem(implies(implies(implies(a, Y2), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.91/11.48  = { by axiom 2 (condensed_detachment) }
% 41.91/11.48    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.91/11.48  = { by axiom 1 (ifeq_axiom) }
% 41.91/11.48    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.91/11.48  = { by axiom 1 (ifeq_axiom) R->L }
% 41.91/11.48    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.91/11.48  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 41.91/11.49    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a)), implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), a), implies(implies(a, b), a))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.91/11.49  = { by axiom 2 (condensed_detachment) }
% 41.91/11.49    ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.91/11.49  = { by axiom 1 (ifeq_axiom) }
% 41.91/11.49    ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.91/11.49  = { by axiom 1 (ifeq_axiom) R->L }
% 41.91/11.49    ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.91/11.49  = { by axiom 2 (condensed_detachment) R->L }
% 41.91/11.49    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true, ifeq(is_a_theorem(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3)))), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.91/11.49  = { by axiom 1 (ifeq_axiom) R->L }
% 41.91/11.49    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.91/11.49  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 41.91/11.49    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3)))), true, is_a_theorem(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 41.91/11.50  = { by axiom 1 (ifeq_axiom) R->L }
% 41.91/11.50    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3)))), true, is_a_theorem(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.11/11.50  = { by axiom 2 (condensed_detachment) R->L }
% 42.11/11.50    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T3, Y3), implies(X3, Y3)), implies(Y3, implies(X3, Y3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3)))), implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(T3, Y3), implies(X3, Y3)), implies(Y3, implies(X3, Y3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))))), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3)))), true, is_a_theorem(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.11/11.50  = { by axiom 1 (ifeq_axiom) R->L }
% 42.11/11.51    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(T3, Y3), implies(X3, Y3)), implies(Y3, implies(X3, Y3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3)))), implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T3, Y3), implies(X3, Y3)), implies(Y3, implies(X3, Y3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))))), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3)))), true, is_a_theorem(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.11/11.51  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 42.11/11.51    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(T3, Y3)), implies(implies(implies(T3, Y3), implies(X3, Y3)), implies(Y3, implies(X3, Y3))))), true, is_a_theorem(implies(implies(implies(implies(implies(T3, Y3), implies(X3, Y3)), implies(Y3, implies(X3, Y3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3)))), implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T3, Y3), implies(X3, Y3)), implies(Y3, implies(X3, Y3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))))), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3)))), true, is_a_theorem(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.11/11.51  = { by axiom 1 (ifeq_axiom) R->L }
% 42.11/11.51    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(T3, Y3)), implies(implies(implies(T3, Y3), implies(X3, Y3)), implies(Y3, implies(X3, Y3))))), true, is_a_theorem(implies(implies(implies(implies(implies(T3, Y3), implies(X3, Y3)), implies(Y3, implies(X3, Y3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3)))), implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T3, Y3), implies(X3, Y3)), implies(Y3, implies(X3, Y3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))))), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3)))), true, is_a_theorem(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.11/11.52  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 42.11/11.52    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(T3, Y3)), implies(implies(implies(T3, Y3), implies(X3, Y3)), implies(Y3, implies(X3, Y3)))), implies(implies(implies(implies(implies(T3, Y3), implies(X3, Y3)), implies(Y3, implies(X3, Y3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3)))), implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(T3, Y3)), implies(implies(implies(T3, Y3), implies(X3, Y3)), implies(Y3, implies(X3, Y3))))), true, is_a_theorem(implies(implies(implies(implies(implies(T3, Y3), implies(X3, Y3)), implies(Y3, implies(X3, Y3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3)))), implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T3, Y3), implies(X3, Y3)), implies(Y3, implies(X3, Y3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))))), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3)))), true, is_a_theorem(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.11/11.52  = { by axiom 2 (condensed_detachment) }
% 42.11/11.52    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(T3, Y3), implies(X3, Y3)), implies(Y3, implies(X3, Y3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))))), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3)))), true, is_a_theorem(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.11/11.53  = { by axiom 1 (ifeq_axiom) }
% 42.11/11.53    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T3, Y3), implies(X3, Y3)), implies(Y3, implies(X3, Y3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))))), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3)))), true, is_a_theorem(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.11/11.53  = { by axiom 1 (ifeq_axiom) R->L }
% 42.11/11.53    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T3, Y3), implies(X3, Y3)), implies(Y3, implies(X3, Y3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3)))), true, is_a_theorem(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.11/11.53  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 42.11/11.53    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y3, implies(X3, Y3)), T3), implies(implies(T3, Y3), implies(X3, Y3)))), true, is_a_theorem(implies(implies(implies(implies(T3, Y3), implies(X3, Y3)), implies(Y3, implies(X3, Y3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3)))), true, is_a_theorem(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.11/11.53  = { by axiom 1 (ifeq_axiom) R->L }
% 42.11/11.54    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y3, implies(X3, Y3)), T3), implies(implies(T3, Y3), implies(X3, Y3)))), true, is_a_theorem(implies(implies(implies(implies(T3, Y3), implies(X3, Y3)), implies(Y3, implies(X3, Y3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3)))), true, is_a_theorem(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.11/11.54  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 42.11/11.54    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y3, implies(X3, Y3)), T3), implies(implies(T3, Y3), implies(X3, Y3))), implies(implies(implies(implies(T3, Y3), implies(X3, Y3)), implies(Y3, implies(X3, Y3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3)))))), true, ifeq(is_a_theorem(implies(implies(implies(Y3, implies(X3, Y3)), T3), implies(implies(T3, Y3), implies(X3, Y3)))), true, is_a_theorem(implies(implies(implies(implies(T3, Y3), implies(X3, Y3)), implies(Y3, implies(X3, Y3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3)))), true, is_a_theorem(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.11/11.54  = { by axiom 2 (condensed_detachment) }
% 42.11/11.54    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3)))), true, is_a_theorem(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.11/11.54  = { by axiom 1 (ifeq_axiom) }
% 42.11/11.54    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))))), true, ifeq(is_a_theorem(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3)))), true, is_a_theorem(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.11/11.54  = { by axiom 2 (condensed_detachment) }
% 42.11/11.54    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.11/11.54  = { by axiom 1 (ifeq_axiom) }
% 42.11/11.55    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.11/11.55  = { by axiom 1 (ifeq_axiom) R->L }
% 42.11/11.55    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.11/11.55  = { by axiom 2 (condensed_detachment) R->L }
% 42.11/11.55    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.11/11.55  = { by axiom 3 (ic_JLukasiewicz) }
% 42.11/11.55    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.11/11.55  = { by axiom 1 (ifeq_axiom) }
% 42.11/11.55    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.11/11.56  = { by axiom 1 (ifeq_axiom) R->L }
% 42.11/11.56    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.11/11.56  = { by axiom 2 (condensed_detachment) R->L }
% 42.11/11.56    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(is_a_theorem(implies(implies(S3, X4), implies(X4, implies(S3, X4)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.11/11.56  = { by axiom 1 (ifeq_axiom) R->L }
% 42.11/11.57    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(S3, X4), implies(X4, implies(S3, X4)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.11/11.57  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 42.11/11.57    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), W4), implies(implies(W4, Y4), implies(V4, Y4)))), true, is_a_theorem(implies(implies(S3, X4), implies(X4, implies(S3, X4)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.11/11.57  = { by axiom 1 (ifeq_axiom) R->L }
% 42.11/11.57    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), W4), implies(implies(W4, Y4), implies(V4, Y4)))), true, is_a_theorem(implies(implies(S3, X4), implies(X4, implies(S3, X4)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.11/11.58  = { by axiom 2 (condensed_detachment) R->L }
% 42.11/11.58    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(U4, X4), implies(S3, X4)), implies(X4, implies(S3, X4))), implies(implies(S3, X4), implies(X4, implies(S3, X4)))), implies(implies(implies(implies(Y4, Z4), W4), implies(implies(W4, Y4), implies(V4, Y4))), implies(implies(S3, X4), implies(X4, implies(S3, X4)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(U4, X4), implies(S3, X4)), implies(X4, implies(S3, X4))), implies(implies(S3, X4), implies(X4, implies(S3, X4))))), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), W4), implies(implies(W4, Y4), implies(V4, Y4))), implies(implies(S3, X4), implies(X4, implies(S3, X4))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), W4), implies(implies(W4, Y4), implies(V4, Y4)))), true, is_a_theorem(implies(implies(S3, X4), implies(X4, implies(S3, X4)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.11/11.59  = { by axiom 1 (ifeq_axiom) R->L }
% 42.11/11.59    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(U4, X4), implies(S3, X4)), implies(X4, implies(S3, X4))), implies(implies(S3, X4), implies(X4, implies(S3, X4)))), implies(implies(implies(implies(Y4, Z4), W4), implies(implies(W4, Y4), implies(V4, Y4))), implies(implies(S3, X4), implies(X4, implies(S3, X4)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U4, X4), implies(S3, X4)), implies(X4, implies(S3, X4))), implies(implies(S3, X4), implies(X4, implies(S3, X4))))), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), W4), implies(implies(W4, Y4), implies(V4, Y4))), implies(implies(S3, X4), implies(X4, implies(S3, X4))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), W4), implies(implies(W4, Y4), implies(V4, Y4)))), true, is_a_theorem(implies(implies(S3, X4), implies(X4, implies(S3, X4)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.11/11.59  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 42.11/11.59    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(U4, X4)), implies(implies(implies(U4, X4), implies(S3, X4)), implies(X4, implies(S3, X4))))), true, is_a_theorem(implies(implies(implies(implies(implies(U4, X4), implies(S3, X4)), implies(X4, implies(S3, X4))), implies(implies(S3, X4), implies(X4, implies(S3, X4)))), implies(implies(implies(implies(Y4, Z4), W4), implies(implies(W4, Y4), implies(V4, Y4))), implies(implies(S3, X4), implies(X4, implies(S3, X4)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U4, X4), implies(S3, X4)), implies(X4, implies(S3, X4))), implies(implies(S3, X4), implies(X4, implies(S3, X4))))), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), W4), implies(implies(W4, Y4), implies(V4, Y4))), implies(implies(S3, X4), implies(X4, implies(S3, X4))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), W4), implies(implies(W4, Y4), implies(V4, Y4)))), true, is_a_theorem(implies(implies(S3, X4), implies(X4, implies(S3, X4)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.11/11.60  = { by axiom 1 (ifeq_axiom) R->L }
% 42.32/11.60    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(U4, X4)), implies(implies(implies(U4, X4), implies(S3, X4)), implies(X4, implies(S3, X4))))), true, is_a_theorem(implies(implies(implies(implies(implies(U4, X4), implies(S3, X4)), implies(X4, implies(S3, X4))), implies(implies(S3, X4), implies(X4, implies(S3, X4)))), implies(implies(implies(implies(Y4, Z4), W4), implies(implies(W4, Y4), implies(V4, Y4))), implies(implies(S3, X4), implies(X4, implies(S3, X4)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U4, X4), implies(S3, X4)), implies(X4, implies(S3, X4))), implies(implies(S3, X4), implies(X4, implies(S3, X4))))), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), W4), implies(implies(W4, Y4), implies(V4, Y4))), implies(implies(S3, X4), implies(X4, implies(S3, X4))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), W4), implies(implies(W4, Y4), implies(V4, Y4)))), true, is_a_theorem(implies(implies(S3, X4), implies(X4, implies(S3, X4)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.32/11.61  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 42.32/11.61    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(U4, X4)), implies(implies(implies(U4, X4), implies(S3, X4)), implies(X4, implies(S3, X4)))), implies(implies(implies(implies(implies(U4, X4), implies(S3, X4)), implies(X4, implies(S3, X4))), implies(implies(S3, X4), implies(X4, implies(S3, X4)))), implies(implies(implies(implies(Y4, Z4), W4), implies(implies(W4, Y4), implies(V4, Y4))), implies(implies(S3, X4), implies(X4, implies(S3, X4))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(U4, X4)), implies(implies(implies(U4, X4), implies(S3, X4)), implies(X4, implies(S3, X4))))), true, is_a_theorem(implies(implies(implies(implies(implies(U4, X4), implies(S3, X4)), implies(X4, implies(S3, X4))), implies(implies(S3, X4), implies(X4, implies(S3, X4)))), implies(implies(implies(implies(Y4, Z4), W4), implies(implies(W4, Y4), implies(V4, Y4))), implies(implies(S3, X4), implies(X4, implies(S3, X4)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U4, X4), implies(S3, X4)), implies(X4, implies(S3, X4))), implies(implies(S3, X4), implies(X4, implies(S3, X4))))), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), W4), implies(implies(W4, Y4), implies(V4, Y4))), implies(implies(S3, X4), implies(X4, implies(S3, X4))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), W4), implies(implies(W4, Y4), implies(V4, Y4)))), true, is_a_theorem(implies(implies(S3, X4), implies(X4, implies(S3, X4)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.32/11.61  = { by axiom 2 (condensed_detachment) }
% 42.32/11.62    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(U4, X4), implies(S3, X4)), implies(X4, implies(S3, X4))), implies(implies(S3, X4), implies(X4, implies(S3, X4))))), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), W4), implies(implies(W4, Y4), implies(V4, Y4))), implies(implies(S3, X4), implies(X4, implies(S3, X4))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), W4), implies(implies(W4, Y4), implies(V4, Y4)))), true, is_a_theorem(implies(implies(S3, X4), implies(X4, implies(S3, X4)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.32/11.62  = { by axiom 1 (ifeq_axiom) }
% 42.32/11.62    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U4, X4), implies(S3, X4)), implies(X4, implies(S3, X4))), implies(implies(S3, X4), implies(X4, implies(S3, X4))))), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), W4), implies(implies(W4, Y4), implies(V4, Y4))), implies(implies(S3, X4), implies(X4, implies(S3, X4))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), W4), implies(implies(W4, Y4), implies(V4, Y4)))), true, is_a_theorem(implies(implies(S3, X4), implies(X4, implies(S3, X4)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.32/11.62  = { by axiom 1 (ifeq_axiom) R->L }
% 42.32/11.63    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U4, X4), implies(S3, X4)), implies(X4, implies(S3, X4))), implies(implies(S3, X4), implies(X4, implies(S3, X4))))), true), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), W4), implies(implies(W4, Y4), implies(V4, Y4))), implies(implies(S3, X4), implies(X4, implies(S3, X4))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), W4), implies(implies(W4, Y4), implies(V4, Y4)))), true, is_a_theorem(implies(implies(S3, X4), implies(X4, implies(S3, X4)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.32/11.63  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 42.32/11.63    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X4, implies(S3, X4)), U4), implies(implies(U4, X4), implies(S3, X4)))), true, is_a_theorem(implies(implies(implies(implies(U4, X4), implies(S3, X4)), implies(X4, implies(S3, X4))), implies(implies(S3, X4), implies(X4, implies(S3, X4))))), true), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), W4), implies(implies(W4, Y4), implies(V4, Y4))), implies(implies(S3, X4), implies(X4, implies(S3, X4))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), W4), implies(implies(W4, Y4), implies(V4, Y4)))), true, is_a_theorem(implies(implies(S3, X4), implies(X4, implies(S3, X4)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.32/11.63  = { by axiom 1 (ifeq_axiom) R->L }
% 42.32/11.63    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X4, implies(S3, X4)), U4), implies(implies(U4, X4), implies(S3, X4)))), true, is_a_theorem(implies(implies(implies(implies(U4, X4), implies(S3, X4)), implies(X4, implies(S3, X4))), implies(implies(S3, X4), implies(X4, implies(S3, X4))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), W4), implies(implies(W4, Y4), implies(V4, Y4))), implies(implies(S3, X4), implies(X4, implies(S3, X4))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), W4), implies(implies(W4, Y4), implies(V4, Y4)))), true, is_a_theorem(implies(implies(S3, X4), implies(X4, implies(S3, X4)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.32/11.64  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 42.32/11.64    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X4, implies(S3, X4)), U4), implies(implies(U4, X4), implies(S3, X4))), implies(implies(implies(implies(U4, X4), implies(S3, X4)), implies(X4, implies(S3, X4))), implies(implies(S3, X4), implies(X4, implies(S3, X4)))))), true, ifeq(is_a_theorem(implies(implies(implies(X4, implies(S3, X4)), U4), implies(implies(U4, X4), implies(S3, X4)))), true, is_a_theorem(implies(implies(implies(implies(U4, X4), implies(S3, X4)), implies(X4, implies(S3, X4))), implies(implies(S3, X4), implies(X4, implies(S3, X4))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), W4), implies(implies(W4, Y4), implies(V4, Y4))), implies(implies(S3, X4), implies(X4, implies(S3, X4))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), W4), implies(implies(W4, Y4), implies(V4, Y4)))), true, is_a_theorem(implies(implies(S3, X4), implies(X4, implies(S3, X4)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.32/11.64  = { by axiom 2 (condensed_detachment) }
% 42.32/11.64    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), W4), implies(implies(W4, Y4), implies(V4, Y4))), implies(implies(S3, X4), implies(X4, implies(S3, X4))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), W4), implies(implies(W4, Y4), implies(V4, Y4)))), true, is_a_theorem(implies(implies(S3, X4), implies(X4, implies(S3, X4)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.32/11.65  = { by axiom 1 (ifeq_axiom) }
% 42.32/11.65    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y4, Z4), W4), implies(implies(W4, Y4), implies(V4, Y4))), implies(implies(S3, X4), implies(X4, implies(S3, X4))))), true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), W4), implies(implies(W4, Y4), implies(V4, Y4)))), true, is_a_theorem(implies(implies(S3, X4), implies(X4, implies(S3, X4)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.32/11.65  = { by axiom 2 (condensed_detachment) }
% 42.32/11.65    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.32/11.66  = { by axiom 1 (ifeq_axiom) }
% 42.32/11.66    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.32/11.66  = { by axiom 1 (ifeq_axiom) R->L }
% 42.32/11.66    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.32/11.66  = { by axiom 2 (condensed_detachment) R->L }
% 42.32/11.67    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.32/11.67  = { by axiom 3 (ic_JLukasiewicz) }
% 42.32/11.67    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.32/11.67  = { by axiom 1 (ifeq_axiom) }
% 42.32/11.68    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.32/11.68  = { by axiom 1 (ifeq_axiom) R->L }
% 42.32/11.68    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.32/11.69  = { by axiom 2 (condensed_detachment) R->L }
% 42.32/11.69    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(is_a_theorem(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.32/11.70  = { by axiom 1 (ifeq_axiom) R->L }
% 42.53/11.70    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.53/11.71  = { by axiom 2 (condensed_detachment) R->L }
% 42.53/11.71    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(a, b), implies(a, b))), implies(Z5, implies(implies(a, b), implies(a, b)))), implies(implies(implies(Z5, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(a, b), implies(a, b))), implies(Z5, implies(implies(a, b), implies(a, b))))), true, is_a_theorem(implies(implies(implies(Z5, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.53/11.72  = { by axiom 3 (ic_JLukasiewicz) }
% 42.53/11.72    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(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(a, b), implies(a, b))), implies(Z5, implies(implies(a, b), implies(a, b))))), true, is_a_theorem(implies(implies(implies(Z5, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.53/11.73  = { by axiom 1 (ifeq_axiom) }
% 42.53/11.73    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(a, b), implies(a, b))), implies(Z5, implies(implies(a, b), implies(a, b))))), true, is_a_theorem(implies(implies(implies(Z5, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.53/11.74  = { by axiom 1 (ifeq_axiom) R->L }
% 42.53/11.74    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(a, b), implies(a, b))), implies(Z5, implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z5, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.53/11.75  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 42.53/11.75    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(a, b), implies(a, b))), implies(Z5, implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z5, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.53/11.76  = { by axiom 1 (ifeq_axiom) R->L }
% 42.53/11.76    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(a, b), implies(a, b))), implies(Z5, implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(Z5, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.53/11.77  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 42.53/11.77    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(a, b), implies(a, b))), implies(Z5, implies(implies(a, b), implies(a, b)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(a, b), implies(a, b))), implies(Z5, implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(Z5, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.53/11.78  = { by axiom 2 (condensed_detachment) }
% 42.53/11.78    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(Z5, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.53/11.79  = { by axiom 1 (ifeq_axiom) }
% 42.53/11.80    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z5, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.73/11.80  = { by axiom 1 (ifeq_axiom) R->L }
% 42.73/11.80    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Z5, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.73/11.81  = { by axiom 2 (condensed_detachment) R->L }
% 42.73/11.82    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), Z5), implies(implies(Z5, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(Z5, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), Z5), implies(implies(Z5, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(Z5, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z5, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.73/11.83  = { by axiom 3 (ic_JLukasiewicz) }
% 42.73/11.83    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(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), Z5), implies(implies(Z5, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(Z5, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z5, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.73/11.84  = { by axiom 1 (ifeq_axiom) }
% 42.73/11.85    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), Z5), implies(implies(Z5, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(Z5, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z5, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.73/11.85  = { by axiom 3 (ic_JLukasiewicz) }
% 42.73/11.85    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z5, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z5, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.73/11.86  = { by axiom 1 (ifeq_axiom) }
% 42.73/11.86    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z5, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(is_a_theorem(implies(implies(implies(Z5, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.73/11.87  = { by axiom 2 (condensed_detachment) }
% 42.73/11.87    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.73/11.87  = { by axiom 1 (ifeq_axiom) }
% 42.73/11.88    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T4, S4), X5), implies(implies(X5, T4), implies(Y5, T4)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.73/11.88  = { by axiom 3 (ic_JLukasiewicz) }
% 42.73/11.88    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.73/11.88  = { by axiom 1 (ifeq_axiom) }
% 42.73/11.89    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.73/11.89  = { by axiom 1 (ifeq_axiom) R->L }
% 42.73/11.89    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.73/11.90  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 42.73/11.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.94/11.90  = { by axiom 2 (condensed_detachment) }
% 42.94/11.91    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.94/11.91  = { by axiom 1 (ifeq_axiom) }
% 42.94/11.91    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.94/11.92  = { by axiom 1 (ifeq_axiom) R->L }
% 42.94/11.92    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.94/11.92  = { by axiom 2 (condensed_detachment) R->L }
% 42.94/11.93    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(is_a_theorem(implies(implies(W5, V5), implies(V5, implies(W5, V5)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.94/11.93  = { by axiom 1 (ifeq_axiom) R->L }
% 42.94/11.93    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(W5, V5), implies(V5, implies(W5, V5)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.94/11.94  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 42.94/11.94    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(U5, T5), S5), implies(implies(S5, U5), implies(X6, U5)))), true, is_a_theorem(implies(implies(W5, V5), implies(V5, implies(W5, V5)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.94/11.95  = { by axiom 1 (ifeq_axiom) R->L }
% 42.94/11.95    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U5, T5), S5), implies(implies(S5, U5), implies(X6, U5)))), true, is_a_theorem(implies(implies(W5, V5), implies(V5, implies(W5, V5)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.94/11.96  = { by axiom 2 (condensed_detachment) R->L }
% 42.94/11.96    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Y6, V5), implies(W5, V5)), implies(V5, implies(W5, V5))), implies(implies(W5, V5), implies(V5, implies(W5, V5)))), implies(implies(implies(implies(U5, T5), S5), implies(implies(S5, U5), implies(X6, U5))), implies(implies(W5, V5), implies(V5, implies(W5, V5)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y6, V5), implies(W5, V5)), implies(V5, implies(W5, V5))), implies(implies(W5, V5), implies(V5, implies(W5, V5))))), true, is_a_theorem(implies(implies(implies(implies(U5, T5), S5), implies(implies(S5, U5), implies(X6, U5))), implies(implies(W5, V5), implies(V5, implies(W5, V5))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U5, T5), S5), implies(implies(S5, U5), implies(X6, U5)))), true, is_a_theorem(implies(implies(W5, V5), implies(V5, implies(W5, V5)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.94/11.97  = { by axiom 1 (ifeq_axiom) R->L }
% 42.94/11.97    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(Y6, V5), implies(W5, V5)), implies(V5, implies(W5, V5))), implies(implies(W5, V5), implies(V5, implies(W5, V5)))), implies(implies(implies(implies(U5, T5), S5), implies(implies(S5, U5), implies(X6, U5))), implies(implies(W5, V5), implies(V5, implies(W5, V5)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y6, V5), implies(W5, V5)), implies(V5, implies(W5, V5))), implies(implies(W5, V5), implies(V5, implies(W5, V5))))), true, is_a_theorem(implies(implies(implies(implies(U5, T5), S5), implies(implies(S5, U5), implies(X6, U5))), implies(implies(W5, V5), implies(V5, implies(W5, V5))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U5, T5), S5), implies(implies(S5, U5), implies(X6, U5)))), true, is_a_theorem(implies(implies(W5, V5), implies(V5, implies(W5, V5)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.94/11.98  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 42.94/11.99    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(Y6, V5)), implies(implies(implies(Y6, V5), implies(W5, V5)), implies(V5, implies(W5, V5))))), true, is_a_theorem(implies(implies(implies(implies(implies(Y6, V5), implies(W5, V5)), implies(V5, implies(W5, V5))), implies(implies(W5, V5), implies(V5, implies(W5, V5)))), implies(implies(implies(implies(U5, T5), S5), implies(implies(S5, U5), implies(X6, U5))), implies(implies(W5, V5), implies(V5, implies(W5, V5)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y6, V5), implies(W5, V5)), implies(V5, implies(W5, V5))), implies(implies(W5, V5), implies(V5, implies(W5, V5))))), true, is_a_theorem(implies(implies(implies(implies(U5, T5), S5), implies(implies(S5, U5), implies(X6, U5))), implies(implies(W5, V5), implies(V5, implies(W5, V5))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U5, T5), S5), implies(implies(S5, U5), implies(X6, U5)))), true, is_a_theorem(implies(implies(W5, V5), implies(V5, implies(W5, V5)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 42.94/11.99  = { by axiom 1 (ifeq_axiom) R->L }
% 42.94/12.00    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(Y6, V5)), implies(implies(implies(Y6, V5), implies(W5, V5)), implies(V5, implies(W5, V5))))), true, is_a_theorem(implies(implies(implies(implies(implies(Y6, V5), implies(W5, V5)), implies(V5, implies(W5, V5))), implies(implies(W5, V5), implies(V5, implies(W5, V5)))), implies(implies(implies(implies(U5, T5), S5), implies(implies(S5, U5), implies(X6, U5))), implies(implies(W5, V5), implies(V5, implies(W5, V5)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y6, V5), implies(W5, V5)), implies(V5, implies(W5, V5))), implies(implies(W5, V5), implies(V5, implies(W5, V5))))), true, is_a_theorem(implies(implies(implies(implies(U5, T5), S5), implies(implies(S5, U5), implies(X6, U5))), implies(implies(W5, V5), implies(V5, implies(W5, V5))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U5, T5), S5), implies(implies(S5, U5), implies(X6, U5)))), true, is_a_theorem(implies(implies(W5, V5), implies(V5, implies(W5, V5)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 43.15/12.01  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 43.15/12.01    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(Y6, V5)), implies(implies(implies(Y6, V5), implies(W5, V5)), implies(V5, implies(W5, V5)))), implies(implies(implies(implies(implies(Y6, V5), implies(W5, V5)), implies(V5, implies(W5, V5))), implies(implies(W5, V5), implies(V5, implies(W5, V5)))), implies(implies(implies(implies(U5, T5), S5), implies(implies(S5, U5), implies(X6, U5))), implies(implies(W5, V5), implies(V5, implies(W5, V5))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(Y6, V5)), implies(implies(implies(Y6, V5), implies(W5, V5)), implies(V5, implies(W5, V5))))), true, is_a_theorem(implies(implies(implies(implies(implies(Y6, V5), implies(W5, V5)), implies(V5, implies(W5, V5))), implies(implies(W5, V5), implies(V5, implies(W5, V5)))), implies(implies(implies(implies(U5, T5), S5), implies(implies(S5, U5), implies(X6, U5))), implies(implies(W5, V5), implies(V5, implies(W5, V5)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y6, V5), implies(W5, V5)), implies(V5, implies(W5, V5))), implies(implies(W5, V5), implies(V5, implies(W5, V5))))), true, is_a_theorem(implies(implies(implies(implies(U5, T5), S5), implies(implies(S5, U5), implies(X6, U5))), implies(implies(W5, V5), implies(V5, implies(W5, V5))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U5, T5), S5), implies(implies(S5, U5), implies(X6, U5)))), true, is_a_theorem(implies(implies(W5, V5), implies(V5, implies(W5, V5)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 43.15/12.02  = { by axiom 2 (condensed_detachment) }
% 43.15/12.02    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Y6, V5), implies(W5, V5)), implies(V5, implies(W5, V5))), implies(implies(W5, V5), implies(V5, implies(W5, V5))))), true, is_a_theorem(implies(implies(implies(implies(U5, T5), S5), implies(implies(S5, U5), implies(X6, U5))), implies(implies(W5, V5), implies(V5, implies(W5, V5))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U5, T5), S5), implies(implies(S5, U5), implies(X6, U5)))), true, is_a_theorem(implies(implies(W5, V5), implies(V5, implies(W5, V5)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 43.15/12.03  = { by axiom 1 (ifeq_axiom) }
% 43.15/12.03    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y6, V5), implies(W5, V5)), implies(V5, implies(W5, V5))), implies(implies(W5, V5), implies(V5, implies(W5, V5))))), true, is_a_theorem(implies(implies(implies(implies(U5, T5), S5), implies(implies(S5, U5), implies(X6, U5))), implies(implies(W5, V5), implies(V5, implies(W5, V5))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U5, T5), S5), implies(implies(S5, U5), implies(X6, U5)))), true, is_a_theorem(implies(implies(W5, V5), implies(V5, implies(W5, V5)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 43.15/12.04  = { by axiom 1 (ifeq_axiom) R->L }
% 43.15/12.04    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y6, V5), implies(W5, V5)), implies(V5, implies(W5, V5))), implies(implies(W5, V5), implies(V5, implies(W5, V5))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), S5), implies(implies(S5, U5), implies(X6, U5))), implies(implies(W5, V5), implies(V5, implies(W5, V5))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U5, T5), S5), implies(implies(S5, U5), implies(X6, U5)))), true, is_a_theorem(implies(implies(W5, V5), implies(V5, implies(W5, V5)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 43.15/12.05  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 43.15/12.05    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V5, implies(W5, V5)), Y6), implies(implies(Y6, V5), implies(W5, V5)))), true, is_a_theorem(implies(implies(implies(implies(Y6, V5), implies(W5, V5)), implies(V5, implies(W5, V5))), implies(implies(W5, V5), implies(V5, implies(W5, V5))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), S5), implies(implies(S5, U5), implies(X6, U5))), implies(implies(W5, V5), implies(V5, implies(W5, V5))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U5, T5), S5), implies(implies(S5, U5), implies(X6, U5)))), true, is_a_theorem(implies(implies(W5, V5), implies(V5, implies(W5, V5)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 43.15/12.06  = { by axiom 1 (ifeq_axiom) R->L }
% 43.15/12.06    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V5, implies(W5, V5)), Y6), implies(implies(Y6, V5), implies(W5, V5)))), true, is_a_theorem(implies(implies(implies(implies(Y6, V5), implies(W5, V5)), implies(V5, implies(W5, V5))), implies(implies(W5, V5), implies(V5, implies(W5, V5))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), S5), implies(implies(S5, U5), implies(X6, U5))), implies(implies(W5, V5), implies(V5, implies(W5, V5))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U5, T5), S5), implies(implies(S5, U5), implies(X6, U5)))), true, is_a_theorem(implies(implies(W5, V5), implies(V5, implies(W5, V5)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 43.15/12.07  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 43.15/12.07    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V5, implies(W5, V5)), Y6), implies(implies(Y6, V5), implies(W5, V5))), implies(implies(implies(implies(Y6, V5), implies(W5, V5)), implies(V5, implies(W5, V5))), implies(implies(W5, V5), implies(V5, implies(W5, V5)))))), true, ifeq(is_a_theorem(implies(implies(implies(V5, implies(W5, V5)), Y6), implies(implies(Y6, V5), implies(W5, V5)))), true, is_a_theorem(implies(implies(implies(implies(Y6, V5), implies(W5, V5)), implies(V5, implies(W5, V5))), implies(implies(W5, V5), implies(V5, implies(W5, V5))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), S5), implies(implies(S5, U5), implies(X6, U5))), implies(implies(W5, V5), implies(V5, implies(W5, V5))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U5, T5), S5), implies(implies(S5, U5), implies(X6, U5)))), true, is_a_theorem(implies(implies(W5, V5), implies(V5, implies(W5, V5)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 43.15/12.08  = { by axiom 2 (condensed_detachment) }
% 43.15/12.08    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U5, T5), S5), implies(implies(S5, U5), implies(X6, U5))), implies(implies(W5, V5), implies(V5, implies(W5, V5))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U5, T5), S5), implies(implies(S5, U5), implies(X6, U5)))), true, is_a_theorem(implies(implies(W5, V5), implies(V5, implies(W5, V5)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 43.36/12.11  = { by axiom 1 (ifeq_axiom) }
% 43.36/12.12    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U5, T5), S5), implies(implies(S5, U5), implies(X6, U5))), implies(implies(W5, V5), implies(V5, implies(W5, V5))))), true, ifeq(is_a_theorem(implies(implies(implies(U5, T5), S5), implies(implies(S5, U5), implies(X6, U5)))), true, is_a_theorem(implies(implies(W5, V5), implies(V5, implies(W5, V5)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 43.36/12.12  = { by axiom 2 (condensed_detachment) }
% 43.36/12.12    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 43.36/12.13  = { by axiom 1 (ifeq_axiom) }
% 43.36/12.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 43.36/12.14  = { by axiom 1 (ifeq_axiom) R->L }
% 43.36/12.14    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 43.36/12.14  = { by axiom 2 (condensed_detachment) R->L }
% 43.36/12.15    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 43.36/12.16  = { by axiom 3 (ic_JLukasiewicz) }
% 43.36/12.16    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 43.36/12.17  = { by axiom 1 (ifeq_axiom) }
% 43.36/12.17    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 43.36/12.18  = { by axiom 1 (ifeq_axiom) R->L }
% 43.36/12.18    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 43.36/12.19  = { by axiom 2 (condensed_detachment) R->L }
% 43.36/12.20    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z6, W6), V6), implies(implies(V6, Z6), implies(U6, Z6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(is_a_theorem(implies(implies(implies(Z6, W6), V6), implies(implies(V6, Z6), implies(U6, Z6)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 43.36/12.21  = { by axiom 1 (ifeq_axiom) R->L }
% 43.36/12.22    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z6, W6), V6), implies(implies(V6, Z6), implies(U6, Z6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z6, W6), V6), implies(implies(V6, Z6), implies(U6, Z6)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 43.36/12.23  = { by axiom 2 (condensed_detachment) R->L }
% 43.36/12.24    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), T6), implies(implies(T6, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(T6, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), T6), implies(implies(T6, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(T6, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z6, W6), V6), implies(implies(V6, Z6), implies(U6, Z6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z6, W6), V6), implies(implies(V6, Z6), implies(U6, Z6)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 43.36/12.25  = { by axiom 3 (ic_JLukasiewicz) }
% 43.36/12.25    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), T6), implies(implies(T6, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(T6, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z6, W6), V6), implies(implies(V6, Z6), implies(U6, Z6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z6, W6), V6), implies(implies(V6, Z6), implies(U6, Z6)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 43.67/12.26  = { by axiom 1 (ifeq_axiom) }
% 43.67/12.27    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), T6), implies(implies(T6, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(T6, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z6, W6), V6), implies(implies(V6, Z6), implies(U6, Z6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z6, W6), V6), implies(implies(V6, Z6), implies(U6, Z6)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 43.67/12.28  = { by axiom 3 (ic_JLukasiewicz) }
% 43.67/12.29    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T6, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z6, W6), V6), implies(implies(V6, Z6), implies(U6, Z6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z6, W6), V6), implies(implies(V6, Z6), implies(U6, Z6)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 43.67/12.31  = { by axiom 1 (ifeq_axiom) }
% 43.67/12.31    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T6, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(Z6, W6), V6), implies(implies(V6, Z6), implies(U6, Z6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z6, W6), V6), implies(implies(V6, Z6), implies(U6, Z6)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 43.67/12.33  = { by axiom 1 (ifeq_axiom) R->L }
% 43.67/12.33    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(T6, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(Z6, W6), V6), implies(implies(V6, Z6), implies(U6, Z6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z6, W6), V6), implies(implies(V6, Z6), implies(U6, Z6)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 43.67/12.35  = { by axiom 2 (condensed_detachment) R->L }
% 43.87/12.36    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(T6, implies(implies(a, b), implies(a, b)))), implies(implies(implies(T6, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), implies(implies(implies(implies(implies(T6, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), implies(implies(implies(implies(Z6, W6), V6), implies(implies(V6, Z6), implies(U6, Z6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(T6, implies(implies(a, b), implies(a, b)))), implies(implies(implies(T6, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(implies(T6, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), implies(implies(implies(implies(Z6, W6), V6), implies(implies(V6, Z6), implies(U6, Z6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T6, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(Z6, W6), V6), implies(implies(V6, Z6), implies(U6, Z6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z6, W6), V6), implies(implies(V6, Z6), implies(U6, Z6)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 43.87/12.37  = { by axiom 3 (ic_JLukasiewicz) }
% 43.87/12.38    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(T6, implies(implies(a, b), implies(a, b)))), implies(implies(implies(T6, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(implies(T6, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), implies(implies(implies(implies(Z6, W6), V6), implies(implies(V6, Z6), implies(U6, Z6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T6, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(Z6, W6), V6), implies(implies(V6, Z6), implies(U6, Z6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z6, W6), V6), implies(implies(V6, Z6), implies(U6, Z6)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 43.87/12.39  = { by axiom 1 (ifeq_axiom) }
% 43.96/12.41    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(T6, implies(implies(a, b), implies(a, b)))), implies(implies(implies(T6, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(implies(T6, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), implies(implies(implies(implies(Z6, W6), V6), implies(implies(V6, Z6), implies(U6, Z6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T6, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(Z6, W6), V6), implies(implies(V6, Z6), implies(U6, Z6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z6, W6), V6), implies(implies(V6, Z6), implies(U6, Z6)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 43.96/12.41  = { by axiom 3 (ic_JLukasiewicz) }
% 43.96/12.42    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(T6, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), implies(implies(implies(implies(Z6, W6), V6), implies(implies(V6, Z6), implies(U6, Z6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T6, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(Z6, W6), V6), implies(implies(V6, Z6), implies(U6, Z6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z6, W6), V6), implies(implies(V6, Z6), implies(U6, Z6)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 43.96/12.43  = { by axiom 1 (ifeq_axiom) }
% 43.96/12.44    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T6, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), implies(implies(implies(implies(Z6, W6), V6), implies(implies(V6, Z6), implies(U6, Z6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(T6, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(Z6, W6), V6), implies(implies(V6, Z6), implies(U6, Z6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z6, W6), V6), implies(implies(V6, Z6), implies(U6, Z6)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 43.96/12.44  = { by axiom 2 (condensed_detachment) }
% 43.96/12.45    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Z6, W6), V6), implies(implies(V6, Z6), implies(U6, Z6)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 43.96/12.45  = { by axiom 1 (ifeq_axiom) }
% 43.96/12.46    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z6, W6), V6), implies(implies(V6, Z6), implies(U6, Z6)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 43.96/12.46  = { by axiom 3 (ic_JLukasiewicz) }
% 43.96/12.47    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 43.96/12.48  = { by axiom 1 (ifeq_axiom) }
% 43.96/12.48    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 43.96/12.49  = { by axiom 1 (ifeq_axiom) R->L }
% 43.96/12.49    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 43.96/12.50  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 44.17/12.50    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.17/12.51  = { by axiom 2 (condensed_detachment) }
% 44.17/12.51    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.17/12.52  = { by axiom 1 (ifeq_axiom) }
% 44.17/12.52    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.17/12.53  = { by axiom 1 (ifeq_axiom) R->L }
% 44.17/12.54    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.17/12.55  = { by axiom 2 (condensed_detachment) R->L }
% 44.17/12.55    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S6, X7), Y7), implies(implies(Y7, S6), implies(Z7, S6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(is_a_theorem(implies(implies(implies(S6, X7), Y7), implies(implies(Y7, S6), implies(Z7, S6)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.17/12.57  = { by axiom 1 (ifeq_axiom) R->L }
% 44.17/12.57    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S6, X7), Y7), implies(implies(Y7, S6), implies(Z7, S6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S6, X7), Y7), implies(implies(Y7, S6), implies(Z7, S6)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.17/12.58  = { by axiom 2 (condensed_detachment) R->L }
% 44.17/12.59    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), W7), implies(implies(W7, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(W7, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), W7), implies(implies(W7, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(W7, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S6, X7), Y7), implies(implies(Y7, S6), implies(Z7, S6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S6, X7), Y7), implies(implies(Y7, S6), implies(Z7, S6)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.36/12.60  = { by axiom 3 (ic_JLukasiewicz) }
% 44.36/12.61    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), W7), implies(implies(W7, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(W7, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S6, X7), Y7), implies(implies(Y7, S6), implies(Z7, S6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S6, X7), Y7), implies(implies(Y7, S6), implies(Z7, S6)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.36/12.62  = { by axiom 1 (ifeq_axiom) }
% 44.36/12.63    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), W7), implies(implies(W7, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(W7, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(implies(S6, X7), Y7), implies(implies(Y7, S6), implies(Z7, S6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S6, X7), Y7), implies(implies(Y7, S6), implies(Z7, S6)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.36/12.64  = { by axiom 3 (ic_JLukasiewicz) }
% 44.36/12.65    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W7, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(implies(S6, X7), Y7), implies(implies(Y7, S6), implies(Z7, S6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S6, X7), Y7), implies(implies(Y7, S6), implies(Z7, S6)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.36/12.66  = { by axiom 1 (ifeq_axiom) }
% 44.36/12.67    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W7, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(S6, X7), Y7), implies(implies(Y7, S6), implies(Z7, S6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S6, X7), Y7), implies(implies(Y7, S6), implies(Z7, S6)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.36/12.68  = { by axiom 1 (ifeq_axiom) R->L }
% 44.36/12.69    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(W7, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(S6, X7), Y7), implies(implies(Y7, S6), implies(Z7, S6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S6, X7), Y7), implies(implies(Y7, S6), implies(Z7, S6)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.57/12.70  = { by axiom 2 (condensed_detachment) R->L }
% 44.57/12.72    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(W7, implies(implies(a, b), implies(a, b)))), implies(implies(implies(W7, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), implies(implies(implies(implies(implies(W7, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), implies(implies(implies(implies(S6, X7), Y7), implies(implies(Y7, S6), implies(Z7, S6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(W7, implies(implies(a, b), implies(a, b)))), implies(implies(implies(W7, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(implies(W7, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), implies(implies(implies(implies(S6, X7), Y7), implies(implies(Y7, S6), implies(Z7, S6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W7, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(S6, X7), Y7), implies(implies(Y7, S6), implies(Z7, S6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S6, X7), Y7), implies(implies(Y7, S6), implies(Z7, S6)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.57/12.74  = { by axiom 3 (ic_JLukasiewicz) }
% 44.57/12.75    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(W7, implies(implies(a, b), implies(a, b)))), implies(implies(implies(W7, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(implies(W7, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), implies(implies(implies(implies(S6, X7), Y7), implies(implies(Y7, S6), implies(Z7, S6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W7, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(S6, X7), Y7), implies(implies(Y7, S6), implies(Z7, S6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S6, X7), Y7), implies(implies(Y7, S6), implies(Z7, S6)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.57/12.76  = { by axiom 1 (ifeq_axiom) }
% 44.57/12.77    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(W7, implies(implies(a, b), implies(a, b)))), implies(implies(implies(W7, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(implies(W7, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), implies(implies(implies(implies(S6, X7), Y7), implies(implies(Y7, S6), implies(Z7, S6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W7, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(S6, X7), Y7), implies(implies(Y7, S6), implies(Z7, S6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S6, X7), Y7), implies(implies(Y7, S6), implies(Z7, S6)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.57/12.78  = { by axiom 3 (ic_JLukasiewicz) }
% 44.57/12.79    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(W7, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), implies(implies(implies(implies(S6, X7), Y7), implies(implies(Y7, S6), implies(Z7, S6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W7, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(S6, X7), Y7), implies(implies(Y7, S6), implies(Z7, S6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S6, X7), Y7), implies(implies(Y7, S6), implies(Z7, S6)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.57/12.79  = { by axiom 1 (ifeq_axiom) }
% 44.74/12.80    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(W7, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), implies(implies(implies(implies(S6, X7), Y7), implies(implies(Y7, S6), implies(Z7, S6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(W7, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(S6, X7), Y7), implies(implies(Y7, S6), implies(Z7, S6))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S6, X7), Y7), implies(implies(Y7, S6), implies(Z7, S6)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.74/12.81  = { by axiom 2 (condensed_detachment) }
% 44.74/12.81    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(S6, X7), Y7), implies(implies(Y7, S6), implies(Z7, S6)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.74/12.82  = { by axiom 1 (ifeq_axiom) }
% 44.74/12.82    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(S6, X7), Y7), implies(implies(Y7, S6), implies(Z7, S6)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.74/12.83  = { by axiom 3 (ic_JLukasiewicz) }
% 44.74/12.83    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.74/12.83  = { by axiom 1 (ifeq_axiom) }
% 44.74/12.84    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(W5, V5), implies(V5, implies(W5, V5))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.74/12.84  = { by axiom 2 (condensed_detachment) }
% 44.74/12.84    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.74/12.84  = { by axiom 1 (ifeq_axiom) }
% 44.74/12.84    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(S3, X4))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.74/12.84  = { by axiom 2 (condensed_detachment) }
% 44.74/12.84    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.74/12.85  = { by axiom 1 (ifeq_axiom) }
% 44.74/12.85    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.74/12.85  = { by axiom 1 (ifeq_axiom) R->L }
% 44.74/12.85    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.74/12.85  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 44.74/12.85    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.74/12.85  = { by axiom 2 (condensed_detachment) }
% 44.74/12.86    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.74/12.86  = { by axiom 1 (ifeq_axiom) }
% 44.74/12.86    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.74/12.86  = { by axiom 1 (ifeq_axiom) R->L }
% 44.74/12.86    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.74/12.86  = { by axiom 2 (condensed_detachment) R->L }
% 44.74/12.86    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(is_a_theorem(implies(implies(V7, U7), implies(U7, implies(V7, U7)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.74/12.87  = { by axiom 1 (ifeq_axiom) R->L }
% 44.74/12.87    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(V7, U7), implies(U7, implies(V7, U7)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.74/12.87  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 44.74/12.87    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(T7, S7), X8), implies(implies(X8, T7), implies(Y8, T7)))), true, is_a_theorem(implies(implies(V7, U7), implies(U7, implies(V7, U7)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.74/12.88  = { by axiom 1 (ifeq_axiom) R->L }
% 44.74/12.88    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T7, S7), X8), implies(implies(X8, T7), implies(Y8, T7)))), true, is_a_theorem(implies(implies(V7, U7), implies(U7, implies(V7, U7)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.74/12.88  = { by axiom 2 (condensed_detachment) R->L }
% 44.74/12.88    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z8, U7), implies(V7, U7)), implies(U7, implies(V7, U7))), implies(implies(V7, U7), implies(U7, implies(V7, U7)))), implies(implies(implies(implies(T7, S7), X8), implies(implies(X8, T7), implies(Y8, T7))), implies(implies(V7, U7), implies(U7, implies(V7, U7)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z8, U7), implies(V7, U7)), implies(U7, implies(V7, U7))), implies(implies(V7, U7), implies(U7, implies(V7, U7))))), true, is_a_theorem(implies(implies(implies(implies(T7, S7), X8), implies(implies(X8, T7), implies(Y8, T7))), implies(implies(V7, U7), implies(U7, implies(V7, U7))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T7, S7), X8), implies(implies(X8, T7), implies(Y8, T7)))), true, is_a_theorem(implies(implies(V7, U7), implies(U7, implies(V7, U7)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.74/12.89  = { by axiom 1 (ifeq_axiom) R->L }
% 44.74/12.89    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(Z8, U7), implies(V7, U7)), implies(U7, implies(V7, U7))), implies(implies(V7, U7), implies(U7, implies(V7, U7)))), implies(implies(implies(implies(T7, S7), X8), implies(implies(X8, T7), implies(Y8, T7))), implies(implies(V7, U7), implies(U7, implies(V7, U7)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z8, U7), implies(V7, U7)), implies(U7, implies(V7, U7))), implies(implies(V7, U7), implies(U7, implies(V7, U7))))), true, is_a_theorem(implies(implies(implies(implies(T7, S7), X8), implies(implies(X8, T7), implies(Y8, T7))), implies(implies(V7, U7), implies(U7, implies(V7, U7))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T7, S7), X8), implies(implies(X8, T7), implies(Y8, T7)))), true, is_a_theorem(implies(implies(V7, U7), implies(U7, implies(V7, U7)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.74/12.90  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 44.84/12.90    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(Z8, U7)), implies(implies(implies(Z8, U7), implies(V7, U7)), implies(U7, implies(V7, U7))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z8, U7), implies(V7, U7)), implies(U7, implies(V7, U7))), implies(implies(V7, U7), implies(U7, implies(V7, U7)))), implies(implies(implies(implies(T7, S7), X8), implies(implies(X8, T7), implies(Y8, T7))), implies(implies(V7, U7), implies(U7, implies(V7, U7)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z8, U7), implies(V7, U7)), implies(U7, implies(V7, U7))), implies(implies(V7, U7), implies(U7, implies(V7, U7))))), true, is_a_theorem(implies(implies(implies(implies(T7, S7), X8), implies(implies(X8, T7), implies(Y8, T7))), implies(implies(V7, U7), implies(U7, implies(V7, U7))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T7, S7), X8), implies(implies(X8, T7), implies(Y8, T7)))), true, is_a_theorem(implies(implies(V7, U7), implies(U7, implies(V7, U7)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.84/12.90  = { by axiom 1 (ifeq_axiom) R->L }
% 44.84/12.91    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(Z8, U7)), implies(implies(implies(Z8, U7), implies(V7, U7)), implies(U7, implies(V7, U7))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z8, U7), implies(V7, U7)), implies(U7, implies(V7, U7))), implies(implies(V7, U7), implies(U7, implies(V7, U7)))), implies(implies(implies(implies(T7, S7), X8), implies(implies(X8, T7), implies(Y8, T7))), implies(implies(V7, U7), implies(U7, implies(V7, U7)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z8, U7), implies(V7, U7)), implies(U7, implies(V7, U7))), implies(implies(V7, U7), implies(U7, implies(V7, U7))))), true, is_a_theorem(implies(implies(implies(implies(T7, S7), X8), implies(implies(X8, T7), implies(Y8, T7))), implies(implies(V7, U7), implies(U7, implies(V7, U7))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T7, S7), X8), implies(implies(X8, T7), implies(Y8, T7)))), true, is_a_theorem(implies(implies(V7, U7), implies(U7, implies(V7, U7)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.84/12.91  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 44.84/12.91    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(Z8, U7)), implies(implies(implies(Z8, U7), implies(V7, U7)), implies(U7, implies(V7, U7)))), implies(implies(implies(implies(implies(Z8, U7), implies(V7, U7)), implies(U7, implies(V7, U7))), implies(implies(V7, U7), implies(U7, implies(V7, U7)))), implies(implies(implies(implies(T7, S7), X8), implies(implies(X8, T7), implies(Y8, T7))), implies(implies(V7, U7), implies(U7, implies(V7, U7))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(Z8, U7)), implies(implies(implies(Z8, U7), implies(V7, U7)), implies(U7, implies(V7, U7))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z8, U7), implies(V7, U7)), implies(U7, implies(V7, U7))), implies(implies(V7, U7), implies(U7, implies(V7, U7)))), implies(implies(implies(implies(T7, S7), X8), implies(implies(X8, T7), implies(Y8, T7))), implies(implies(V7, U7), implies(U7, implies(V7, U7)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z8, U7), implies(V7, U7)), implies(U7, implies(V7, U7))), implies(implies(V7, U7), implies(U7, implies(V7, U7))))), true, is_a_theorem(implies(implies(implies(implies(T7, S7), X8), implies(implies(X8, T7), implies(Y8, T7))), implies(implies(V7, U7), implies(U7, implies(V7, U7))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T7, S7), X8), implies(implies(X8, T7), implies(Y8, T7)))), true, is_a_theorem(implies(implies(V7, U7), implies(U7, implies(V7, U7)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.84/12.92  = { by axiom 2 (condensed_detachment) }
% 44.84/12.92    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Z8, U7), implies(V7, U7)), implies(U7, implies(V7, U7))), implies(implies(V7, U7), implies(U7, implies(V7, U7))))), true, is_a_theorem(implies(implies(implies(implies(T7, S7), X8), implies(implies(X8, T7), implies(Y8, T7))), implies(implies(V7, U7), implies(U7, implies(V7, U7))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T7, S7), X8), implies(implies(X8, T7), implies(Y8, T7)))), true, is_a_theorem(implies(implies(V7, U7), implies(U7, implies(V7, U7)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.84/12.92  = { by axiom 1 (ifeq_axiom) }
% 44.84/12.92    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z8, U7), implies(V7, U7)), implies(U7, implies(V7, U7))), implies(implies(V7, U7), implies(U7, implies(V7, U7))))), true, is_a_theorem(implies(implies(implies(implies(T7, S7), X8), implies(implies(X8, T7), implies(Y8, T7))), implies(implies(V7, U7), implies(U7, implies(V7, U7))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T7, S7), X8), implies(implies(X8, T7), implies(Y8, T7)))), true, is_a_theorem(implies(implies(V7, U7), implies(U7, implies(V7, U7)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.84/12.93  = { by axiom 1 (ifeq_axiom) R->L }
% 44.84/12.93    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z8, U7), implies(V7, U7)), implies(U7, implies(V7, U7))), implies(implies(V7, U7), implies(U7, implies(V7, U7))))), true), true, is_a_theorem(implies(implies(implies(implies(T7, S7), X8), implies(implies(X8, T7), implies(Y8, T7))), implies(implies(V7, U7), implies(U7, implies(V7, U7))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T7, S7), X8), implies(implies(X8, T7), implies(Y8, T7)))), true, is_a_theorem(implies(implies(V7, U7), implies(U7, implies(V7, U7)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.84/12.93  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 44.84/12.93    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U7, implies(V7, U7)), Z8), implies(implies(Z8, U7), implies(V7, U7)))), true, is_a_theorem(implies(implies(implies(implies(Z8, U7), implies(V7, U7)), implies(U7, implies(V7, U7))), implies(implies(V7, U7), implies(U7, implies(V7, U7))))), true), true, is_a_theorem(implies(implies(implies(implies(T7, S7), X8), implies(implies(X8, T7), implies(Y8, T7))), implies(implies(V7, U7), implies(U7, implies(V7, U7))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T7, S7), X8), implies(implies(X8, T7), implies(Y8, T7)))), true, is_a_theorem(implies(implies(V7, U7), implies(U7, implies(V7, U7)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.84/12.94  = { by axiom 1 (ifeq_axiom) R->L }
% 44.84/12.94    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U7, implies(V7, U7)), Z8), implies(implies(Z8, U7), implies(V7, U7)))), true, is_a_theorem(implies(implies(implies(implies(Z8, U7), implies(V7, U7)), implies(U7, implies(V7, U7))), implies(implies(V7, U7), implies(U7, implies(V7, U7))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T7, S7), X8), implies(implies(X8, T7), implies(Y8, T7))), implies(implies(V7, U7), implies(U7, implies(V7, U7))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T7, S7), X8), implies(implies(X8, T7), implies(Y8, T7)))), true, is_a_theorem(implies(implies(V7, U7), implies(U7, implies(V7, U7)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.84/12.94  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 44.84/12.94    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U7, implies(V7, U7)), Z8), implies(implies(Z8, U7), implies(V7, U7))), implies(implies(implies(implies(Z8, U7), implies(V7, U7)), implies(U7, implies(V7, U7))), implies(implies(V7, U7), implies(U7, implies(V7, U7)))))), true, ifeq(is_a_theorem(implies(implies(implies(U7, implies(V7, U7)), Z8), implies(implies(Z8, U7), implies(V7, U7)))), true, is_a_theorem(implies(implies(implies(implies(Z8, U7), implies(V7, U7)), implies(U7, implies(V7, U7))), implies(implies(V7, U7), implies(U7, implies(V7, U7))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T7, S7), X8), implies(implies(X8, T7), implies(Y8, T7))), implies(implies(V7, U7), implies(U7, implies(V7, U7))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T7, S7), X8), implies(implies(X8, T7), implies(Y8, T7)))), true, is_a_theorem(implies(implies(V7, U7), implies(U7, implies(V7, U7)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.84/12.95  = { by axiom 2 (condensed_detachment) }
% 44.84/12.95    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T7, S7), X8), implies(implies(X8, T7), implies(Y8, T7))), implies(implies(V7, U7), implies(U7, implies(V7, U7))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T7, S7), X8), implies(implies(X8, T7), implies(Y8, T7)))), true, is_a_theorem(implies(implies(V7, U7), implies(U7, implies(V7, U7)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.84/12.95  = { by axiom 1 (ifeq_axiom) }
% 44.84/12.95    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T7, S7), X8), implies(implies(X8, T7), implies(Y8, T7))), implies(implies(V7, U7), implies(U7, implies(V7, U7))))), true, ifeq(is_a_theorem(implies(implies(implies(T7, S7), X8), implies(implies(X8, T7), implies(Y8, T7)))), true, is_a_theorem(implies(implies(V7, U7), implies(U7, implies(V7, U7)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.84/12.95  = { by axiom 2 (condensed_detachment) }
% 44.84/12.95    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.84/12.96  = { by axiom 1 (ifeq_axiom) }
% 44.84/12.96    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.84/12.96  = { by axiom 1 (ifeq_axiom) R->L }
% 44.84/12.96    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.84/12.96  = { by axiom 2 (condensed_detachment) R->L }
% 44.84/12.97    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.84/12.97  = { by axiom 3 (ic_JLukasiewicz) }
% 44.84/12.97    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.84/12.98  = { by axiom 1 (ifeq_axiom) }
% 44.84/12.98    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.84/12.98  = { by axiom 1 (ifeq_axiom) R->L }
% 44.84/12.99    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.84/12.99  = { by axiom 2 (condensed_detachment) R->L }
% 44.84/12.99    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(is_a_theorem(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.84/13.00  = { by axiom 1 (ifeq_axiom) R->L }
% 44.95/13.00    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.95/13.01  = { by axiom 2 (condensed_detachment) R->L }
% 44.95/13.01    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(a, b), implies(a, b))), implies(S8, implies(implies(a, b), implies(a, b)))), implies(implies(implies(S8, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(a, b), implies(a, b))), implies(S8, implies(implies(a, b), implies(a, b))))), true, is_a_theorem(implies(implies(implies(S8, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.95/13.02  = { by axiom 3 (ic_JLukasiewicz) }
% 44.95/13.02    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(a, b), implies(a, b))), implies(S8, implies(implies(a, b), implies(a, b))))), true, is_a_theorem(implies(implies(implies(S8, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.95/13.03  = { by axiom 1 (ifeq_axiom) }
% 44.95/13.03    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(a, b), implies(a, b))), implies(S8, implies(implies(a, b), implies(a, b))))), true, is_a_theorem(implies(implies(implies(S8, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.95/13.04  = { by axiom 1 (ifeq_axiom) R->L }
% 44.95/13.04    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(a, b), implies(a, b))), implies(S8, implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S8, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.95/13.05  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 44.95/13.05    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(a, b), implies(a, b))), implies(S8, implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(S8, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.95/13.05  = { by axiom 1 (ifeq_axiom) R->L }
% 44.95/13.07    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(a, b), implies(a, b))), implies(S8, implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(S8, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.95/13.08  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 44.95/13.08    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(a, b), implies(a, b))), implies(S8, implies(implies(a, b), implies(a, b)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(a, b), implies(a, b))), implies(S8, implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(S8, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.95/13.09  = { by axiom 2 (condensed_detachment) }
% 44.95/13.09    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(S8, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 44.95/13.10  = { by axiom 1 (ifeq_axiom) }
% 44.95/13.10    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S8, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.05/13.11  = { by axiom 1 (ifeq_axiom) R->L }
% 45.05/13.11    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(S8, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.05/13.12  = { by axiom 2 (condensed_detachment) R->L }
% 45.05/13.12    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), S8), implies(implies(S8, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(S8, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), S8), implies(implies(S8, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(S8, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S8, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.05/13.13  = { by axiom 3 (ic_JLukasiewicz) }
% 45.05/13.14    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), S8), implies(implies(S8, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(S8, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S8, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.05/13.14  = { by axiom 1 (ifeq_axiom) }
% 45.05/13.15    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), S8), implies(implies(S8, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(S8, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S8, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.05/13.15  = { by axiom 3 (ic_JLukasiewicz) }
% 45.05/13.15    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S8, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S8, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.05/13.16  = { by axiom 1 (ifeq_axiom) }
% 45.05/13.16    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S8, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(is_a_theorem(implies(implies(implies(S8, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.05/13.17  = { by axiom 2 (condensed_detachment) }
% 45.05/13.17    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.05/13.17  = { by axiom 1 (ifeq_axiom) }
% 45.05/13.17    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), U8), implies(implies(U8, W8), implies(T8, W8)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.05/13.18  = { by axiom 3 (ic_JLukasiewicz) }
% 45.05/13.18    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.05/13.18  = { by axiom 1 (ifeq_axiom) }
% 45.05/13.18    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.05/13.19  = { by axiom 1 (ifeq_axiom) R->L }
% 45.05/13.19    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.05/13.19  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 45.05/13.19    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.05/13.20  = { by axiom 2 (condensed_detachment) }
% 45.05/13.20    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.05/13.20  = { by axiom 1 (ifeq_axiom) }
% 45.05/13.21    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.05/13.21  = { by axiom 1 (ifeq_axiom) R->L }
% 45.05/13.21    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.05/13.22  = { by axiom 2 (condensed_detachment) R->L }
% 45.05/13.22    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(is_a_theorem(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.05/13.22  = { by axiom 1 (ifeq_axiom) R->L }
% 45.05/13.23    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.05/13.23  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 45.05/13.24    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z9, W9), V9), implies(implies(V9, Z9), implies(U9, Z9)))), true, is_a_theorem(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.05/13.24  = { by axiom 1 (ifeq_axiom) R->L }
% 45.05/13.24    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Z9, W9), V9), implies(implies(V9, Z9), implies(U9, Z9)))), true, is_a_theorem(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.05/13.25  = { by axiom 2 (condensed_detachment) R->L }
% 45.05/13.25    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T9, Y9), implies(X9, Y9)), implies(Y9, implies(X9, Y9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9)))), implies(implies(implies(implies(Z9, W9), V9), implies(implies(V9, Z9), implies(U9, Z9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(T9, Y9), implies(X9, Y9)), implies(Y9, implies(X9, Y9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))))), true, is_a_theorem(implies(implies(implies(implies(Z9, W9), V9), implies(implies(V9, Z9), implies(U9, Z9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z9, W9), V9), implies(implies(V9, Z9), implies(U9, Z9)))), true, is_a_theorem(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.22/13.26  = { by axiom 1 (ifeq_axiom) R->L }
% 45.22/13.26    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(T9, Y9), implies(X9, Y9)), implies(Y9, implies(X9, Y9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9)))), implies(implies(implies(implies(Z9, W9), V9), implies(implies(V9, Z9), implies(U9, Z9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T9, Y9), implies(X9, Y9)), implies(Y9, implies(X9, Y9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))))), true, is_a_theorem(implies(implies(implies(implies(Z9, W9), V9), implies(implies(V9, Z9), implies(U9, Z9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z9, W9), V9), implies(implies(V9, Z9), implies(U9, Z9)))), true, is_a_theorem(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.22/13.27  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 45.22/13.28    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(T9, Y9)), implies(implies(implies(T9, Y9), implies(X9, Y9)), implies(Y9, implies(X9, Y9))))), true, is_a_theorem(implies(implies(implies(implies(implies(T9, Y9), implies(X9, Y9)), implies(Y9, implies(X9, Y9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9)))), implies(implies(implies(implies(Z9, W9), V9), implies(implies(V9, Z9), implies(U9, Z9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T9, Y9), implies(X9, Y9)), implies(Y9, implies(X9, Y9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))))), true, is_a_theorem(implies(implies(implies(implies(Z9, W9), V9), implies(implies(V9, Z9), implies(U9, Z9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z9, W9), V9), implies(implies(V9, Z9), implies(U9, Z9)))), true, is_a_theorem(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.22/13.28  = { by axiom 1 (ifeq_axiom) R->L }
% 45.22/13.29    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(T9, Y9)), implies(implies(implies(T9, Y9), implies(X9, Y9)), implies(Y9, implies(X9, Y9))))), true, is_a_theorem(implies(implies(implies(implies(implies(T9, Y9), implies(X9, Y9)), implies(Y9, implies(X9, Y9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9)))), implies(implies(implies(implies(Z9, W9), V9), implies(implies(V9, Z9), implies(U9, Z9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T9, Y9), implies(X9, Y9)), implies(Y9, implies(X9, Y9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))))), true, is_a_theorem(implies(implies(implies(implies(Z9, W9), V9), implies(implies(V9, Z9), implies(U9, Z9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z9, W9), V9), implies(implies(V9, Z9), implies(U9, Z9)))), true, is_a_theorem(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.22/13.29  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 45.22/13.30    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(T9, Y9)), implies(implies(implies(T9, Y9), implies(X9, Y9)), implies(Y9, implies(X9, Y9)))), implies(implies(implies(implies(implies(T9, Y9), implies(X9, Y9)), implies(Y9, implies(X9, Y9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9)))), implies(implies(implies(implies(Z9, W9), V9), implies(implies(V9, Z9), implies(U9, Z9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(T9, Y9)), implies(implies(implies(T9, Y9), implies(X9, Y9)), implies(Y9, implies(X9, Y9))))), true, is_a_theorem(implies(implies(implies(implies(implies(T9, Y9), implies(X9, Y9)), implies(Y9, implies(X9, Y9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9)))), implies(implies(implies(implies(Z9, W9), V9), implies(implies(V9, Z9), implies(U9, Z9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T9, Y9), implies(X9, Y9)), implies(Y9, implies(X9, Y9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))))), true, is_a_theorem(implies(implies(implies(implies(Z9, W9), V9), implies(implies(V9, Z9), implies(U9, Z9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z9, W9), V9), implies(implies(V9, Z9), implies(U9, Z9)))), true, is_a_theorem(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.22/13.30  = { by axiom 2 (condensed_detachment) }
% 45.22/13.31    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(T9, Y9), implies(X9, Y9)), implies(Y9, implies(X9, Y9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))))), true, is_a_theorem(implies(implies(implies(implies(Z9, W9), V9), implies(implies(V9, Z9), implies(U9, Z9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z9, W9), V9), implies(implies(V9, Z9), implies(U9, Z9)))), true, is_a_theorem(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.22/13.31  = { by axiom 1 (ifeq_axiom) }
% 45.22/13.32    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T9, Y9), implies(X9, Y9)), implies(Y9, implies(X9, Y9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))))), true, is_a_theorem(implies(implies(implies(implies(Z9, W9), V9), implies(implies(V9, Z9), implies(U9, Z9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z9, W9), V9), implies(implies(V9, Z9), implies(U9, Z9)))), true, is_a_theorem(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.22/13.32  = { by axiom 1 (ifeq_axiom) R->L }
% 45.22/13.33    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T9, Y9), implies(X9, Y9)), implies(Y9, implies(X9, Y9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))))), true), true, is_a_theorem(implies(implies(implies(implies(Z9, W9), V9), implies(implies(V9, Z9), implies(U9, Z9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z9, W9), V9), implies(implies(V9, Z9), implies(U9, Z9)))), true, is_a_theorem(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.22/13.33  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 45.22/13.34    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y9, implies(X9, Y9)), T9), implies(implies(T9, Y9), implies(X9, Y9)))), true, is_a_theorem(implies(implies(implies(implies(T9, Y9), implies(X9, Y9)), implies(Y9, implies(X9, Y9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))))), true), true, is_a_theorem(implies(implies(implies(implies(Z9, W9), V9), implies(implies(V9, Z9), implies(U9, Z9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z9, W9), V9), implies(implies(V9, Z9), implies(U9, Z9)))), true, is_a_theorem(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.22/13.34  = { by axiom 1 (ifeq_axiom) R->L }
% 45.22/13.34    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y9, implies(X9, Y9)), T9), implies(implies(T9, Y9), implies(X9, Y9)))), true, is_a_theorem(implies(implies(implies(implies(T9, Y9), implies(X9, Y9)), implies(Y9, implies(X9, Y9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z9, W9), V9), implies(implies(V9, Z9), implies(U9, Z9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z9, W9), V9), implies(implies(V9, Z9), implies(U9, Z9)))), true, is_a_theorem(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.22/13.35  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 45.32/13.36    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y9, implies(X9, Y9)), T9), implies(implies(T9, Y9), implies(X9, Y9))), implies(implies(implies(implies(T9, Y9), implies(X9, Y9)), implies(Y9, implies(X9, Y9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9)))))), true, ifeq(is_a_theorem(implies(implies(implies(Y9, implies(X9, Y9)), T9), implies(implies(T9, Y9), implies(X9, Y9)))), true, is_a_theorem(implies(implies(implies(implies(T9, Y9), implies(X9, Y9)), implies(Y9, implies(X9, Y9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z9, W9), V9), implies(implies(V9, Z9), implies(U9, Z9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z9, W9), V9), implies(implies(V9, Z9), implies(U9, Z9)))), true, is_a_theorem(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.32/13.36  = { by axiom 2 (condensed_detachment) }
% 45.32/13.36    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z9, W9), V9), implies(implies(V9, Z9), implies(U9, Z9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z9, W9), V9), implies(implies(V9, Z9), implies(U9, Z9)))), true, is_a_theorem(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.32/13.37  = { by axiom 1 (ifeq_axiom) }
% 45.32/13.37    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z9, W9), V9), implies(implies(V9, Z9), implies(U9, Z9))), implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))))), true, ifeq(is_a_theorem(implies(implies(implies(Z9, W9), V9), implies(implies(V9, Z9), implies(U9, Z9)))), true, is_a_theorem(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.32/13.38  = { by axiom 2 (condensed_detachment) }
% 45.32/13.38    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.32/13.38  = { by axiom 1 (ifeq_axiom) }
% 45.32/13.38    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.32/13.39  = { by axiom 1 (ifeq_axiom) R->L }
% 45.32/13.39    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.32/13.40  = { by axiom 2 (condensed_detachment) R->L }
% 45.36/13.41    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.36/13.41  = { by axiom 3 (ic_JLukasiewicz) }
% 45.36/13.41    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.36/13.42  = { by axiom 1 (ifeq_axiom) }
% 45.36/13.42    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.36/13.43  = { by axiom 1 (ifeq_axiom) R->L }
% 45.36/13.44    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.36/13.45  = { by axiom 2 (condensed_detachment) R->L }
% 45.36/13.46    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S9, X10), Y10), implies(implies(Y10, S9), implies(Z10, S9))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(is_a_theorem(implies(implies(implies(S9, X10), Y10), implies(implies(Y10, S9), implies(Z10, S9)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.36/13.46  = { by axiom 1 (ifeq_axiom) R->L }
% 45.36/13.47    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S9, X10), Y10), implies(implies(Y10, S9), implies(Z10, S9))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S9, X10), Y10), implies(implies(Y10, S9), implies(Z10, S9)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.36/13.48  = { by axiom 2 (condensed_detachment) R->L }
% 45.36/13.49    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), W10), implies(implies(W10, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(W10, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), W10), implies(implies(W10, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(W10, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S9, X10), Y10), implies(implies(Y10, S9), implies(Z10, S9))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S9, X10), Y10), implies(implies(Y10, S9), implies(Z10, S9)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.47/13.50  = { by axiom 3 (ic_JLukasiewicz) }
% 45.47/13.51    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), W10), implies(implies(W10, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(W10, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S9, X10), Y10), implies(implies(Y10, S9), implies(Z10, S9))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S9, X10), Y10), implies(implies(Y10, S9), implies(Z10, S9)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.47/13.52  = { by axiom 1 (ifeq_axiom) }
% 45.47/13.53    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), W10), implies(implies(W10, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(W10, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(implies(S9, X10), Y10), implies(implies(Y10, S9), implies(Z10, S9))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S9, X10), Y10), implies(implies(Y10, S9), implies(Z10, S9)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.47/13.54  = { by axiom 3 (ic_JLukasiewicz) }
% 45.47/13.54    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W10, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(implies(S9, X10), Y10), implies(implies(Y10, S9), implies(Z10, S9))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S9, X10), Y10), implies(implies(Y10, S9), implies(Z10, S9)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.47/13.56  = { by axiom 1 (ifeq_axiom) }
% 45.47/13.57    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W10, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(S9, X10), Y10), implies(implies(Y10, S9), implies(Z10, S9))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S9, X10), Y10), implies(implies(Y10, S9), implies(Z10, S9)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.47/13.58  = { by axiom 1 (ifeq_axiom) R->L }
% 45.47/13.59    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(W10, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(S9, X10), Y10), implies(implies(Y10, S9), implies(Z10, S9))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S9, X10), Y10), implies(implies(Y10, S9), implies(Z10, S9)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.47/13.60  = { by axiom 2 (condensed_detachment) R->L }
% 45.57/13.62    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(W10, implies(implies(a, b), implies(a, b)))), implies(implies(implies(W10, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), implies(implies(implies(implies(implies(W10, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), implies(implies(implies(implies(S9, X10), Y10), implies(implies(Y10, S9), implies(Z10, S9))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(W10, implies(implies(a, b), implies(a, b)))), implies(implies(implies(W10, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(implies(W10, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), implies(implies(implies(implies(S9, X10), Y10), implies(implies(Y10, S9), implies(Z10, S9))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W10, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(S9, X10), Y10), implies(implies(Y10, S9), implies(Z10, S9))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S9, X10), Y10), implies(implies(Y10, S9), implies(Z10, S9)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.57/13.63  = { by axiom 3 (ic_JLukasiewicz) }
% 45.57/13.64    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(W10, implies(implies(a, b), implies(a, b)))), implies(implies(implies(W10, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(implies(W10, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), implies(implies(implies(implies(S9, X10), Y10), implies(implies(Y10, S9), implies(Z10, S9))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W10, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(S9, X10), Y10), implies(implies(Y10, S9), implies(Z10, S9))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S9, X10), Y10), implies(implies(Y10, S9), implies(Z10, S9)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.57/13.65  = { by axiom 1 (ifeq_axiom) }
% 45.57/13.66    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(W10, implies(implies(a, b), implies(a, b)))), implies(implies(implies(W10, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(implies(W10, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), implies(implies(implies(implies(S9, X10), Y10), implies(implies(Y10, S9), implies(Z10, S9))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W10, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(S9, X10), Y10), implies(implies(Y10, S9), implies(Z10, S9))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S9, X10), Y10), implies(implies(Y10, S9), implies(Z10, S9)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.57/13.67  = { by axiom 3 (ic_JLukasiewicz) }
% 45.57/13.68    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(W10, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), implies(implies(implies(implies(S9, X10), Y10), implies(implies(Y10, S9), implies(Z10, S9))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W10, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(S9, X10), Y10), implies(implies(Y10, S9), implies(Z10, S9))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S9, X10), Y10), implies(implies(Y10, S9), implies(Z10, S9)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.57/13.68  = { by axiom 1 (ifeq_axiom) }
% 45.57/13.69    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(W10, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), implies(implies(implies(implies(S9, X10), Y10), implies(implies(Y10, S9), implies(Z10, S9))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(W10, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(S9, X10), Y10), implies(implies(Y10, S9), implies(Z10, S9))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S9, X10), Y10), implies(implies(Y10, S9), implies(Z10, S9)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.57/13.70  = { by axiom 2 (condensed_detachment) }
% 45.68/13.70    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(S9, X10), Y10), implies(implies(Y10, S9), implies(Z10, S9)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.68/13.71  = { by axiom 1 (ifeq_axiom) }
% 45.68/13.72    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S9, X10), Y10), implies(implies(Y10, S9), implies(Z10, S9)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.68/13.72  = { by axiom 3 (ic_JLukasiewicz) }
% 45.68/13.73    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.68/13.73  = { by axiom 1 (ifeq_axiom) }
% 45.68/13.74    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.68/13.74  = { by axiom 1 (ifeq_axiom) R->L }
% 45.68/13.75    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.68/13.75  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 45.68/13.76    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.68/13.77  = { by axiom 2 (condensed_detachment) }
% 45.68/13.77    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.68/13.78  = { by axiom 1 (ifeq_axiom) }
% 45.68/13.78    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.78/13.80  = { by axiom 1 (ifeq_axiom) R->L }
% 45.78/13.81    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.78/13.82  = { by axiom 2 (condensed_detachment) R->L }
% 45.78/13.82    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V10, U10), T10), implies(implies(T10, V10), implies(S10, V10))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(is_a_theorem(implies(implies(implies(V10, U10), T10), implies(implies(T10, V10), implies(S10, V10)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.78/13.83  = { by axiom 1 (ifeq_axiom) R->L }
% 45.78/13.84    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V10, U10), T10), implies(implies(T10, V10), implies(S10, V10))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V10, U10), T10), implies(implies(T10, V10), implies(S10, V10)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.78/13.85  = { by axiom 2 (condensed_detachment) R->L }
% 45.78/13.86    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), X11), implies(implies(X11, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(X11, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), X11), implies(implies(X11, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(X11, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(V10, U10), T10), implies(implies(T10, V10), implies(S10, V10))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V10, U10), T10), implies(implies(T10, V10), implies(S10, V10)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.78/13.87  = { by axiom 3 (ic_JLukasiewicz) }
% 45.78/13.87    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), X11), implies(implies(X11, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(X11, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(V10, U10), T10), implies(implies(T10, V10), implies(S10, V10))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V10, U10), T10), implies(implies(T10, V10), implies(S10, V10)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.78/13.88  = { by axiom 1 (ifeq_axiom) }
% 45.78/13.89    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), X11), implies(implies(X11, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(X11, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(implies(V10, U10), T10), implies(implies(T10, V10), implies(S10, V10))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V10, U10), T10), implies(implies(T10, V10), implies(S10, V10)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.88/13.90  = { by axiom 3 (ic_JLukasiewicz) }
% 45.88/13.91    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X11, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(implies(V10, U10), T10), implies(implies(T10, V10), implies(S10, V10))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V10, U10), T10), implies(implies(T10, V10), implies(S10, V10)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.88/13.92  = { by axiom 1 (ifeq_axiom) }
% 45.88/13.93    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X11, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(V10, U10), T10), implies(implies(T10, V10), implies(S10, V10))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V10, U10), T10), implies(implies(T10, V10), implies(S10, V10)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.88/13.94  = { by axiom 1 (ifeq_axiom) R->L }
% 45.88/13.95    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(X11, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(V10, U10), T10), implies(implies(T10, V10), implies(S10, V10))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V10, U10), T10), implies(implies(T10, V10), implies(S10, V10)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.88/13.96  = { by axiom 2 (condensed_detachment) R->L }
% 45.88/13.98    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(X11, implies(implies(a, b), implies(a, b)))), implies(implies(implies(X11, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), implies(implies(implies(implies(implies(X11, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), implies(implies(implies(implies(V10, U10), T10), implies(implies(T10, V10), implies(S10, V10))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(X11, implies(implies(a, b), implies(a, b)))), implies(implies(implies(X11, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(implies(X11, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), implies(implies(implies(implies(V10, U10), T10), implies(implies(T10, V10), implies(S10, V10))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X11, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(V10, U10), T10), implies(implies(T10, V10), implies(S10, V10))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V10, U10), T10), implies(implies(T10, V10), implies(S10, V10)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.88/13.99  = { by axiom 3 (ic_JLukasiewicz) }
% 45.99/14.00    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(X11, implies(implies(a, b), implies(a, b)))), implies(implies(implies(X11, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(implies(X11, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), implies(implies(implies(implies(V10, U10), T10), implies(implies(T10, V10), implies(S10, V10))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X11, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(V10, U10), T10), implies(implies(T10, V10), implies(S10, V10))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V10, U10), T10), implies(implies(T10, V10), implies(S10, V10)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.99/14.01  = { by axiom 1 (ifeq_axiom) }
% 45.99/14.02    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(X11, implies(implies(a, b), implies(a, b)))), implies(implies(implies(X11, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(implies(X11, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), implies(implies(implies(implies(V10, U10), T10), implies(implies(T10, V10), implies(S10, V10))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X11, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(V10, U10), T10), implies(implies(T10, V10), implies(S10, V10))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V10, U10), T10), implies(implies(T10, V10), implies(S10, V10)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.99/14.03  = { by axiom 3 (ic_JLukasiewicz) }
% 45.99/14.04    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(X11, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), implies(implies(implies(implies(V10, U10), T10), implies(implies(T10, V10), implies(S10, V10))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X11, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(V10, U10), T10), implies(implies(T10, V10), implies(S10, V10))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V10, U10), T10), implies(implies(T10, V10), implies(S10, V10)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.99/14.05  = { by axiom 1 (ifeq_axiom) }
% 45.99/14.06    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(X11, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), implies(implies(implies(implies(V10, U10), T10), implies(implies(T10, V10), implies(S10, V10))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(X11, implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(V10, U10), T10), implies(implies(T10, V10), implies(S10, V10))), implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V10, U10), T10), implies(implies(T10, V10), implies(S10, V10)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.99/14.06  = { by axiom 2 (condensed_detachment) }
% 45.99/14.07    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V10, U10), T10), implies(implies(T10, V10), implies(S10, V10)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.99/14.07  = { by axiom 1 (ifeq_axiom) }
% 45.99/14.08    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(V10, U10), T10), implies(implies(T10, V10), implies(S10, V10)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.99/14.08  = { by axiom 3 (ic_JLukasiewicz) }
% 45.99/14.08    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.99/14.08  = { by axiom 1 (ifeq_axiom) }
% 45.99/14.09    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(X9, Y9), implies(Y9, implies(X9, Y9))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.99/14.09  = { by axiom 2 (condensed_detachment) }
% 45.99/14.09    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.99/14.09  = { by axiom 1 (ifeq_axiom) }
% 45.99/14.09    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, is_a_theorem(implies(implies(implies(V7, U7), implies(U7, implies(V7, U7))), implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.99/14.10  = { by axiom 2 (condensed_detachment) }
% 45.99/14.10    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.99/14.10  = { by axiom 1 (ifeq_axiom) }
% 45.99/14.10    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b))), implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b))))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(a, b), implies(a, b)))), true, is_a_theorem(implies(implies(implies(X3, Y3), implies(Y3, implies(X3, Y3))), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.99/14.10  = { by axiom 2 (condensed_detachment) }
% 45.99/14.10    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 45.99/14.10  = { by axiom 1 (ifeq_axiom) }
% 46.09/14.10    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, b), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 46.09/14.10  = { by axiom 1 (ifeq_axiom) R->L }
% 46.09/14.10    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, b), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 46.09/14.10  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 46.09/14.10    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a)))), true, ifeq(is_a_theorem(implies(implies(a, b), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 46.09/14.10  = { by axiom 2 (condensed_detachment) }
% 46.09/14.10    ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 46.09/14.10  = { by axiom 1 (ifeq_axiom) }
% 46.09/14.10    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 46.09/14.10  = { by axiom 1 (ifeq_axiom) R->L }
% 46.09/14.10    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 46.09/14.10  = { by axiom 2 (condensed_detachment) R->L }
% 46.09/14.11    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y11, Z11), W11), implies(implies(W11, Y11), implies(V11, Y11))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true, ifeq(is_a_theorem(implies(implies(implies(Y11, Z11), W11), implies(implies(W11, Y11), implies(V11, Y11)))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 46.09/14.11  = { by axiom 1 (ifeq_axiom) R->L }
% 46.09/14.11    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y11, Z11), W11), implies(implies(W11, Y11), implies(V11, Y11))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y11, Z11), W11), implies(implies(W11, Y11), implies(V11, Y11)))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 46.09/14.11  = { by axiom 2 (condensed_detachment) R->L }
% 46.09/14.11    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y, implies(X, Y)), U11), implies(implies(U11, Y), implies(X, Y))), implies(implies(implies(implies(U11, 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)), U11), implies(implies(U11, Y), implies(X, Y)))), true, is_a_theorem(implies(implies(implies(implies(U11, 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(Y11, Z11), W11), implies(implies(W11, Y11), implies(V11, Y11))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y11, Z11), W11), implies(implies(W11, Y11), implies(V11, Y11)))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 46.09/14.11  = { by axiom 3 (ic_JLukasiewicz) }
% 46.09/14.11    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y, implies(X, Y)), U11), implies(implies(U11, Y), implies(X, Y)))), true, is_a_theorem(implies(implies(implies(implies(U11, 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(Y11, Z11), W11), implies(implies(W11, Y11), implies(V11, Y11))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y11, Z11), W11), implies(implies(W11, Y11), implies(V11, Y11)))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 46.09/14.11  = { by axiom 1 (ifeq_axiom) }
% 46.09/14.11    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y, implies(X, Y)), U11), implies(implies(U11, Y), implies(X, Y)))), true, is_a_theorem(implies(implies(implies(implies(U11, 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(Y11, Z11), W11), implies(implies(W11, Y11), implies(V11, Y11))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y11, Z11), W11), implies(implies(W11, Y11), implies(V11, Y11)))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 46.09/14.11  = { by axiom 3 (ic_JLukasiewicz) }
% 46.09/14.11    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U11, 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(Y11, Z11), W11), implies(implies(W11, Y11), implies(V11, Y11))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y11, Z11), W11), implies(implies(W11, Y11), implies(V11, Y11)))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 46.09/14.12  = { by axiom 1 (ifeq_axiom) }
% 46.09/14.12    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U11, 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(Y11, Z11), W11), implies(implies(W11, Y11), implies(V11, Y11))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y11, Z11), W11), implies(implies(W11, Y11), implies(V11, Y11)))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 46.09/14.12  = { by axiom 1 (ifeq_axiom) R->L }
% 46.09/14.12    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(U11, 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(Y11, Z11), W11), implies(implies(W11, Y11), implies(V11, Y11))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y11, Z11), W11), implies(implies(W11, Y11), implies(V11, Y11)))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 46.09/14.12  = { by axiom 2 (condensed_detachment) R->L }
% 46.09/14.12    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(U11, Y)), implies(implies(implies(U11, Y), implies(X, Y)), implies(Y, implies(X, Y)))), implies(implies(implies(implies(implies(U11, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(Y11, Z11), W11), implies(implies(W11, Y11), implies(V11, Y11))), 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(U11, Y)), implies(implies(implies(U11, Y), implies(X, Y)), implies(Y, implies(X, Y))))), true, is_a_theorem(implies(implies(implies(implies(implies(U11, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(Y11, Z11), W11), implies(implies(W11, Y11), implies(V11, Y11))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U11, 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(Y11, Z11), W11), implies(implies(W11, Y11), implies(V11, Y11))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y11, Z11), W11), implies(implies(W11, Y11), implies(V11, Y11)))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 46.09/14.12  = { by axiom 3 (ic_JLukasiewicz) }
% 46.09/14.12    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(U11, Y)), implies(implies(implies(U11, Y), implies(X, Y)), implies(Y, implies(X, Y))))), true, is_a_theorem(implies(implies(implies(implies(implies(U11, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(Y11, Z11), W11), implies(implies(W11, Y11), implies(V11, Y11))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U11, 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(Y11, Z11), W11), implies(implies(W11, Y11), implies(V11, Y11))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y11, Z11), W11), implies(implies(W11, Y11), implies(V11, Y11)))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 46.09/14.13  = { by axiom 1 (ifeq_axiom) }
% 46.09/14.13    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(U11, Y)), implies(implies(implies(U11, Y), implies(X, Y)), implies(Y, implies(X, Y))))), true, is_a_theorem(implies(implies(implies(implies(implies(U11, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(Y11, Z11), W11), implies(implies(W11, Y11), implies(V11, Y11))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U11, 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(Y11, Z11), W11), implies(implies(W11, Y11), implies(V11, Y11))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y11, Z11), W11), implies(implies(W11, Y11), implies(V11, Y11)))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 46.09/14.13  = { by axiom 3 (ic_JLukasiewicz) }
% 46.09/14.13    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(U11, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(Y11, Z11), W11), implies(implies(W11, Y11), implies(V11, Y11))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U11, 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(Y11, Z11), W11), implies(implies(W11, Y11), implies(V11, Y11))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y11, Z11), W11), implies(implies(W11, Y11), implies(V11, Y11)))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 46.09/14.13  = { by axiom 1 (ifeq_axiom) }
% 46.09/14.13    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(U11, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(Y11, Z11), W11), implies(implies(W11, Y11), implies(V11, Y11))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(U11, 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(Y11, Z11), W11), implies(implies(W11, Y11), implies(V11, Y11))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y11, Z11), W11), implies(implies(W11, Y11), implies(V11, Y11)))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 46.09/14.13  = { by axiom 2 (condensed_detachment) }
% 46.09/14.13    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y11, Z11), W11), implies(implies(W11, Y11), implies(V11, Y11)))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 46.09/14.13  = { by axiom 1 (ifeq_axiom) }
% 46.09/14.13    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Y11, Z11), W11), implies(implies(W11, Y11), implies(V11, Y11)))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 46.09/14.13  = { by axiom 3 (ic_JLukasiewicz) }
% 46.09/14.13    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), 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(implies(implies(a, b), a), a)), true), true)
% 46.09/14.13  = { by axiom 1 (ifeq_axiom) }
% 46.09/14.13    ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), a), a))), true, ifeq(is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 46.09/14.13  = { by axiom 2 (condensed_detachment) }
% 46.09/14.13    true
% 46.09/14.13  % SZS output end Proof
% 46.09/14.13  
% 46.09/14.13  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------