%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL094-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:49:01 AM UTC 2026
% Result : Unsatisfiable 1.54s 0.66s
% Output : Proof 41.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL094-1 : 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 : n020.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 15:22:34 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.54/0.66 Command-line arguments: --no-flatten-goal
% 1.54/0.66
% 1.54/0.66 % SZS status Unsatisfiable
% 1.54/0.66
% 36.19/7.36 % SZS output start Proof
% 36.19/7.36 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 36.19/7.36 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.
% 36.50/7.49 Axiom 3 (ic_JLukasiewicz_4): is_a_theorem(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X))))) = true.
% 36.50/7.49
% 36.50/7.49 Goal 1 (prove_ic_5): is_a_theorem(implies(a, implies(implies(a, b), b))) = true.
% 36.50/7.49 Proof:
% 36.50/7.49 is_a_theorem(implies(a, implies(implies(a, b), b)))
% 36.50/7.49 = { by axiom 1 (ifeq_axiom) R->L }
% 36.50/7.49 ifeq(true, true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.50/7.49 = { by axiom 2 (condensed_detachment) R->L }
% 36.50/7.50 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, ifeq(is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.50/7.50 = { by axiom 1 (ifeq_axiom) R->L }
% 36.50/7.50 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), 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), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.50/7.50 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 36.50/7.50 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.50/7.50 = { by axiom 1 (ifeq_axiom) R->L }
% 36.81/7.50 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.50 = { by axiom 2 (condensed_detachment) R->L }
% 36.81/7.50 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(S, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(S, 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(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.50 = { by axiom 1 (ifeq_axiom) R->L }
% 36.81/7.50 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(S, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S, 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(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.50 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 36.81/7.50 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(V2, implies(implies(W2, X2), implies(Z2, X2))))), true, is_a_theorem(implies(implies(implies(implies(implies(S, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S, 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(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.51 = { by axiom 1 (ifeq_axiom) R->L }
% 36.81/7.51 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(V2, implies(implies(W2, X2), implies(Z2, X2))))), true, is_a_theorem(implies(implies(implies(implies(implies(S, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S, 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(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.51 = { by axiom 2 (condensed_detachment) R->L }
% 36.81/7.51 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(Y, implies(S, Y))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(implies(S, Y), implies(X, Y)), implies(Y, implies(X, Y))))), implies(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(V2, implies(implies(W2, X2), implies(Z2, X2)))), implies(implies(implies(implies(implies(S, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(X, Y), implies(Y, implies(X, Y)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(Y, implies(S, Y))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(implies(S, Y), implies(X, Y)), implies(Y, implies(X, Y)))))), true, is_a_theorem(implies(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(V2, implies(implies(W2, X2), implies(Z2, X2)))), implies(implies(implies(implies(implies(S, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(X, Y), implies(Y, implies(X, Y))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(V2, implies(implies(W2, X2), implies(Z2, X2))))), true, is_a_theorem(implies(implies(implies(implies(implies(S, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S, 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(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.51 = { by axiom 3 (ic_JLukasiewicz_4) }
% 36.81/7.51 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(Y, implies(S, Y))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(implies(S, Y), implies(X, Y)), implies(Y, implies(X, Y)))))), true, is_a_theorem(implies(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(V2, implies(implies(W2, X2), implies(Z2, X2)))), implies(implies(implies(implies(implies(S, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(X, Y), implies(Y, implies(X, Y))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(V2, implies(implies(W2, X2), implies(Z2, X2))))), true, is_a_theorem(implies(implies(implies(implies(implies(S, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S, 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(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.51 = { by axiom 1 (ifeq_axiom) }
% 36.81/7.52 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(Y, implies(S, Y))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(implies(S, Y), implies(X, Y)), implies(Y, implies(X, Y)))))), true, is_a_theorem(implies(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(V2, implies(implies(W2, X2), implies(Z2, X2)))), implies(implies(implies(implies(implies(S, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(X, Y), implies(Y, implies(X, Y))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(V2, implies(implies(W2, X2), implies(Z2, X2))))), true, is_a_theorem(implies(implies(implies(implies(implies(S, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S, 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(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.52 = { by axiom 3 (ic_JLukasiewicz_4) }
% 36.81/7.52 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(V2, implies(implies(W2, X2), implies(Z2, X2)))), implies(implies(implies(implies(implies(S, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(X, Y), implies(Y, implies(X, Y))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(V2, implies(implies(W2, X2), implies(Z2, X2))))), true, is_a_theorem(implies(implies(implies(implies(implies(S, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S, 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(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.52 = { by axiom 1 (ifeq_axiom) }
% 36.81/7.52 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(V2, implies(implies(W2, X2), implies(Z2, X2)))), implies(implies(implies(implies(implies(S, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(X, Y), implies(Y, implies(X, Y))))))), true, ifeq(is_a_theorem(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(V2, implies(implies(W2, X2), implies(Z2, X2))))), true, is_a_theorem(implies(implies(implies(implies(implies(S, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S, 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(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.52 = { by axiom 2 (condensed_detachment) }
% 36.81/7.52 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(S, 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(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.52 = { by axiom 1 (ifeq_axiom) }
% 36.81/7.52 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S, 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(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.52 = { by axiom 1 (ifeq_axiom) R->L }
% 36.81/7.53 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S, 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(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.53 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 36.81/7.53 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U2, T2), implies(S2, X3)), implies(Y3, implies(implies(X3, U2), implies(S2, U2))))), true, is_a_theorem(implies(implies(implies(implies(S, 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(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.53 = { by axiom 1 (ifeq_axiom) R->L }
% 36.81/7.53 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U2, T2), implies(S2, X3)), implies(Y3, implies(implies(X3, U2), implies(S2, U2))))), true, is_a_theorem(implies(implies(implies(implies(S, 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(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.53 = { by axiom 2 (condensed_detachment) R->L }
% 36.81/7.53 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y, implies(X, Y)), implies(X, S)), implies(implies(X, Y), implies(implies(S, Y), implies(X, Y)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(Y3, implies(implies(X3, U2), implies(S2, U2)))), implies(implies(implies(implies(S, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))))), true, ifeq(is_a_theorem(implies(implies(implies(Y, implies(X, Y)), implies(X, S)), implies(implies(X, Y), implies(implies(S, Y), implies(X, Y))))), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(Y3, implies(implies(X3, U2), implies(S2, U2)))), implies(implies(implies(implies(S, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U2, T2), implies(S2, X3)), implies(Y3, implies(implies(X3, U2), implies(S2, U2))))), true, is_a_theorem(implies(implies(implies(implies(S, 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(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.53 = { by axiom 3 (ic_JLukasiewicz_4) }
% 36.81/7.53 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y, implies(X, Y)), implies(X, S)), implies(implies(X, Y), implies(implies(S, Y), implies(X, Y))))), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(Y3, implies(implies(X3, U2), implies(S2, U2)))), implies(implies(implies(implies(S, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U2, T2), implies(S2, X3)), implies(Y3, implies(implies(X3, U2), implies(S2, U2))))), true, is_a_theorem(implies(implies(implies(implies(S, 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(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.53 = { by axiom 1 (ifeq_axiom) }
% 36.81/7.54 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y, implies(X, Y)), implies(X, S)), implies(implies(X, Y), implies(implies(S, Y), implies(X, Y))))), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(Y3, implies(implies(X3, U2), implies(S2, U2)))), implies(implies(implies(implies(S, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U2, T2), implies(S2, X3)), implies(Y3, implies(implies(X3, U2), implies(S2, U2))))), true, is_a_theorem(implies(implies(implies(implies(S, 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(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.54 = { by axiom 3 (ic_JLukasiewicz_4) }
% 36.81/7.54 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(Y3, implies(implies(X3, U2), implies(S2, U2)))), implies(implies(implies(implies(S, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U2, T2), implies(S2, X3)), implies(Y3, implies(implies(X3, U2), implies(S2, U2))))), true, is_a_theorem(implies(implies(implies(implies(S, 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(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.54 = { by axiom 1 (ifeq_axiom) }
% 36.81/7.54 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(Y3, implies(implies(X3, U2), implies(S2, U2)))), implies(implies(implies(implies(S, 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(U2, T2), implies(S2, X3)), implies(Y3, implies(implies(X3, U2), implies(S2, U2))))), true, is_a_theorem(implies(implies(implies(implies(S, 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(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.54 = { by axiom 2 (condensed_detachment) }
% 36.81/7.54 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.54 = { by axiom 1 (ifeq_axiom) }
% 36.81/7.54 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true, ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.54 = { by axiom 2 (condensed_detachment) }
% 36.81/7.54 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.54 = { by axiom 1 (ifeq_axiom) }
% 36.81/7.54 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.54 = { by axiom 1 (ifeq_axiom) R->L }
% 36.81/7.54 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.54 = { by axiom 2 (condensed_detachment) R->L }
% 36.81/7.54 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(is_a_theorem(implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.54 = { by axiom 1 (ifeq_axiom) R->L }
% 36.81/7.55 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.55 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 36.81/7.55 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3))))), true, is_a_theorem(implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.55 = { by axiom 1 (ifeq_axiom) R->L }
% 36.81/7.55 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3))))), true, is_a_theorem(implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.55 = { by axiom 2 (condensed_detachment) R->L }
% 36.81/7.55 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true, is_a_theorem(implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3))))), true, is_a_theorem(implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.55 = { by axiom 1 (ifeq_axiom) R->L }
% 36.81/7.56 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true, is_a_theorem(implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3))))), true, is_a_theorem(implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.56 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 36.81/7.56 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z4, W4), implies(V4, U4)), implies(T4, implies(implies(U4, Z4), implies(V4, Z4))))), true, is_a_theorem(implies(implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true, is_a_theorem(implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3))))), true, is_a_theorem(implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.56 = { by axiom 1 (ifeq_axiom) R->L }
% 36.81/7.56 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Z4, W4), implies(V4, U4)), implies(T4, implies(implies(U4, Z4), implies(V4, Z4))))), true, is_a_theorem(implies(implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true, is_a_theorem(implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3))))), true, is_a_theorem(implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.57 = { by axiom 2 (condensed_detachment) R->L }
% 36.81/7.57 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(W3, implies(Y4, W3))), implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))))), implies(implies(implies(implies(Z4, W4), implies(V4, U4)), implies(T4, implies(implies(U4, Z4), implies(V4, Z4)))), implies(implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(W3, implies(Y4, W3))), implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3)))))), true, is_a_theorem(implies(implies(implies(implies(Z4, W4), implies(V4, U4)), implies(T4, implies(implies(U4, Z4), implies(V4, Z4)))), implies(implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z4, W4), implies(V4, U4)), implies(T4, implies(implies(U4, Z4), implies(V4, Z4))))), true, is_a_theorem(implies(implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true, is_a_theorem(implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3))))), true, is_a_theorem(implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.57 = { by axiom 3 (ic_JLukasiewicz_4) }
% 36.81/7.57 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(W3, implies(Y4, W3))), implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3)))))), true, is_a_theorem(implies(implies(implies(implies(Z4, W4), implies(V4, U4)), implies(T4, implies(implies(U4, Z4), implies(V4, Z4)))), implies(implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z4, W4), implies(V4, U4)), implies(T4, implies(implies(U4, Z4), implies(V4, Z4))))), true, is_a_theorem(implies(implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true, is_a_theorem(implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3))))), true, is_a_theorem(implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.57 = { by axiom 1 (ifeq_axiom) }
% 36.81/7.58 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(W3, implies(Y4, W3))), implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3)))))), true, is_a_theorem(implies(implies(implies(implies(Z4, W4), implies(V4, U4)), implies(T4, implies(implies(U4, Z4), implies(V4, Z4)))), implies(implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z4, W4), implies(V4, U4)), implies(T4, implies(implies(U4, Z4), implies(V4, Z4))))), true, is_a_theorem(implies(implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true, is_a_theorem(implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3))))), true, is_a_theorem(implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.58 = { by axiom 3 (ic_JLukasiewicz_4) }
% 36.81/7.58 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z4, W4), implies(V4, U4)), implies(T4, implies(implies(U4, Z4), implies(V4, Z4)))), implies(implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z4, W4), implies(V4, U4)), implies(T4, implies(implies(U4, Z4), implies(V4, Z4))))), true, is_a_theorem(implies(implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true, is_a_theorem(implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3))))), true, is_a_theorem(implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.58 = { by axiom 1 (ifeq_axiom) }
% 36.81/7.58 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z4, W4), implies(V4, U4)), implies(T4, implies(implies(U4, Z4), implies(V4, Z4)))), implies(implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))))), true, ifeq(is_a_theorem(implies(implies(implies(Z4, W4), implies(V4, U4)), implies(T4, implies(implies(U4, Z4), implies(V4, Z4))))), true, is_a_theorem(implies(implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true, is_a_theorem(implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3))))), true, is_a_theorem(implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.58 = { by axiom 2 (condensed_detachment) }
% 36.81/7.58 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true, is_a_theorem(implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3))))), true, is_a_theorem(implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.59 = { by axiom 1 (ifeq_axiom) }
% 36.81/7.59 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true, is_a_theorem(implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3))))), true, is_a_theorem(implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.59 = { by axiom 1 (ifeq_axiom) R->L }
% 36.81/7.59 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true), true, is_a_theorem(implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3))))), true, is_a_theorem(implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.59 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 36.81/7.59 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S4, X5), implies(Y5, Z5)), implies(W5, implies(implies(Z5, S4), implies(Y5, S4))))), true, is_a_theorem(implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true), true, is_a_theorem(implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3))))), true, is_a_theorem(implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.59 = { by axiom 1 (ifeq_axiom) R->L }
% 36.81/7.59 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(S4, X5), implies(Y5, Z5)), implies(W5, implies(implies(Z5, S4), implies(Y5, S4))))), true, is_a_theorem(implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true), true), true, is_a_theorem(implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3))))), true, is_a_theorem(implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 36.81/7.60 = { by axiom 2 (condensed_detachment) R->L }
% 36.81/7.60 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W3, implies(Z3, W3)), implies(Z3, Y4)), implies(implies(Z3, W3), implies(implies(Y4, W3), implies(Z3, W3)))), implies(implies(implies(implies(S4, X5), implies(Y5, Z5)), implies(W5, implies(implies(Z5, S4), implies(Y5, S4)))), implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))))), true, ifeq(is_a_theorem(implies(implies(implies(W3, implies(Z3, W3)), implies(Z3, Y4)), implies(implies(Z3, W3), implies(implies(Y4, W3), implies(Z3, W3))))), true, is_a_theorem(implies(implies(implies(implies(S4, X5), implies(Y5, Z5)), implies(W5, implies(implies(Z5, S4), implies(Y5, S4)))), implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S4, X5), implies(Y5, Z5)), implies(W5, implies(implies(Z5, S4), implies(Y5, S4))))), true, is_a_theorem(implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true), true), true, is_a_theorem(implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3))))), true, is_a_theorem(implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.05/7.60 = { by axiom 3 (ic_JLukasiewicz_4) }
% 37.05/7.60 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W3, implies(Z3, W3)), implies(Z3, Y4)), implies(implies(Z3, W3), implies(implies(Y4, W3), implies(Z3, W3))))), true, is_a_theorem(implies(implies(implies(implies(S4, X5), implies(Y5, Z5)), implies(W5, implies(implies(Z5, S4), implies(Y5, S4)))), implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S4, X5), implies(Y5, Z5)), implies(W5, implies(implies(Z5, S4), implies(Y5, S4))))), true, is_a_theorem(implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true), true), true, is_a_theorem(implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3))))), true, is_a_theorem(implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.05/7.60 = { by axiom 1 (ifeq_axiom) }
% 37.05/7.60 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W3, implies(Z3, W3)), implies(Z3, Y4)), implies(implies(Z3, W3), implies(implies(Y4, W3), implies(Z3, W3))))), true, is_a_theorem(implies(implies(implies(implies(S4, X5), implies(Y5, Z5)), implies(W5, implies(implies(Z5, S4), implies(Y5, S4)))), implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S4, X5), implies(Y5, Z5)), implies(W5, implies(implies(Z5, S4), implies(Y5, S4))))), true, is_a_theorem(implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true), true), true, is_a_theorem(implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3))))), true, is_a_theorem(implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.05/7.61 = { by axiom 3 (ic_JLukasiewicz_4) }
% 37.05/7.61 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S4, X5), implies(Y5, Z5)), implies(W5, implies(implies(Z5, S4), implies(Y5, S4)))), implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S4, X5), implies(Y5, Z5)), implies(W5, implies(implies(Z5, S4), implies(Y5, S4))))), true, is_a_theorem(implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true), true), true, is_a_theorem(implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3))))), true, is_a_theorem(implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.05/7.61 = { by axiom 1 (ifeq_axiom) }
% 37.05/7.61 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S4, X5), implies(Y5, Z5)), implies(W5, implies(implies(Z5, S4), implies(Y5, S4)))), implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))))), true, ifeq(is_a_theorem(implies(implies(implies(S4, X5), implies(Y5, Z5)), implies(W5, implies(implies(Z5, S4), implies(Y5, S4))))), true, is_a_theorem(implies(implies(implies(implies(Y4, W3), implies(Z3, W3)), implies(W3, implies(Z3, W3))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true), true), true, is_a_theorem(implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3))))), true, is_a_theorem(implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.05/7.61 = { by axiom 2 (condensed_detachment) }
% 37.05/7.61 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3))))), true, is_a_theorem(implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.05/7.61 = { by axiom 1 (ifeq_axiom) }
% 37.05/7.61 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(Z3, W3), implies(W3, implies(Z3, W3))))), true, ifeq(is_a_theorem(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3))))), true, is_a_theorem(implies(implies(Z3, W3), implies(W3, implies(Z3, W3)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.05/7.61 = { by axiom 2 (condensed_detachment) }
% 37.05/7.61 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.05/7.61 = { by axiom 1 (ifeq_axiom) }
% 37.05/7.61 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.05/7.62 = { by axiom 1 (ifeq_axiom) R->L }
% 37.05/7.62 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.05/7.62 = { by axiom 2 (condensed_detachment) R->L }
% 37.05/7.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true, ifeq(is_a_theorem(implies(implies(V5, U5), implies(U5, implies(V5, U5)))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.05/7.62 = { by axiom 1 (ifeq_axiom) R->L }
% 37.05/7.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(V5, U5), implies(U5, implies(V5, U5)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.05/7.62 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 37.05/7.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(V5, U5), implies(U5, implies(V5, U5)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.05/7.63 = { by axiom 1 (ifeq_axiom) R->L }
% 37.05/7.63 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(V5, U5), implies(U5, implies(V5, U5)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.05/7.63 = { by axiom 2 (condensed_detachment) R->L }
% 37.05/7.63 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5)))), implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(V5, U5), implies(U5, implies(V5, U5)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true, is_a_theorem(implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(V5, U5), implies(U5, implies(V5, U5)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.05/7.63 = { by axiom 1 (ifeq_axiom) R->L }
% 37.05/7.63 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5)))), implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(V5, U5), implies(U5, implies(V5, U5)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true, is_a_theorem(implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(V5, U5), implies(U5, implies(V5, U5)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.05/7.64 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 37.05/7.64 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V6, U6), implies(T6, S6)), implies(X7, implies(implies(S6, V6), implies(T6, V6))))), true, is_a_theorem(implies(implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5)))), implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(V5, U5), implies(U5, implies(V5, U5)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true, is_a_theorem(implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(V5, U5), implies(U5, implies(V5, U5)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.05/7.64 = { by axiom 1 (ifeq_axiom) R->L }
% 37.05/7.64 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V6, U6), implies(T6, S6)), implies(X7, implies(implies(S6, V6), implies(T6, V6))))), true, is_a_theorem(implies(implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5)))), implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(V5, U5), implies(U5, implies(V5, U5)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true, is_a_theorem(implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(V5, U5), implies(U5, implies(V5, U5)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.05/7.65 = { by axiom 2 (condensed_detachment) R->L }
% 37.05/7.65 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(U5, implies(W6, U5))), implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(X7, implies(implies(S6, V6), implies(T6, V6)))), implies(implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5)))), implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(V5, U5), implies(U5, implies(V5, U5)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(U5, implies(W6, U5))), implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5)))))), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(X7, implies(implies(S6, V6), implies(T6, V6)))), implies(implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5)))), implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V6, U6), implies(T6, S6)), implies(X7, implies(implies(S6, V6), implies(T6, V6))))), true, is_a_theorem(implies(implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5)))), implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(V5, U5), implies(U5, implies(V5, U5)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true, is_a_theorem(implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(V5, U5), implies(U5, implies(V5, U5)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.05/7.65 = { by axiom 3 (ic_JLukasiewicz_4) }
% 37.05/7.65 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(U5, implies(W6, U5))), implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5)))))), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(X7, implies(implies(S6, V6), implies(T6, V6)))), implies(implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5)))), implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V6, U6), implies(T6, S6)), implies(X7, implies(implies(S6, V6), implies(T6, V6))))), true, is_a_theorem(implies(implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5)))), implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(V5, U5), implies(U5, implies(V5, U5)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true, is_a_theorem(implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(V5, U5), implies(U5, implies(V5, U5)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.05/7.66 = { by axiom 1 (ifeq_axiom) }
% 37.05/7.66 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(U5, implies(W6, U5))), implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5)))))), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(X7, implies(implies(S6, V6), implies(T6, V6)))), implies(implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5)))), implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V6, U6), implies(T6, S6)), implies(X7, implies(implies(S6, V6), implies(T6, V6))))), true, is_a_theorem(implies(implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5)))), implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(V5, U5), implies(U5, implies(V5, U5)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true, is_a_theorem(implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(V5, U5), implies(U5, implies(V5, U5)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.05/7.66 = { by axiom 3 (ic_JLukasiewicz_4) }
% 37.05/7.66 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(X7, implies(implies(S6, V6), implies(T6, V6)))), implies(implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5)))), implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V6, U6), implies(T6, S6)), implies(X7, implies(implies(S6, V6), implies(T6, V6))))), true, is_a_theorem(implies(implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5)))), implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(V5, U5), implies(U5, implies(V5, U5)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true, is_a_theorem(implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(V5, U5), implies(U5, implies(V5, U5)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.05/7.66 = { by axiom 1 (ifeq_axiom) }
% 37.05/7.67 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(X7, implies(implies(S6, V6), implies(T6, V6)))), implies(implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5)))), implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))))), true, ifeq(is_a_theorem(implies(implies(implies(V6, U6), implies(T6, S6)), implies(X7, implies(implies(S6, V6), implies(T6, V6))))), true, is_a_theorem(implies(implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5)))), implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(V5, U5), implies(U5, implies(V5, U5)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true, is_a_theorem(implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(V5, U5), implies(U5, implies(V5, U5)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.05/7.67 = { by axiom 2 (condensed_detachment) }
% 37.05/7.67 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true, is_a_theorem(implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(V5, U5), implies(U5, implies(V5, U5)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.05/7.67 = { by axiom 1 (ifeq_axiom) }
% 37.05/7.67 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true, is_a_theorem(implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(V5, U5), implies(U5, implies(V5, U5)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.05/7.67 = { by axiom 1 (ifeq_axiom) R->L }
% 37.05/7.68 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true), true, is_a_theorem(implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(V5, U5), implies(U5, implies(V5, U5)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.05/7.68 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 37.05/7.68 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y7, Z7), implies(W7, V7)), implies(U7, implies(implies(V7, Y7), implies(W7, Y7))))), true, is_a_theorem(implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true), true, is_a_theorem(implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(V5, U5), implies(U5, implies(V5, U5)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.05/7.68 = { by axiom 1 (ifeq_axiom) R->L }
% 37.05/7.68 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y7, Z7), implies(W7, V7)), implies(U7, implies(implies(V7, Y7), implies(W7, Y7))))), true, is_a_theorem(implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(V5, U5), implies(U5, implies(V5, U5)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.05/7.69 = { by axiom 2 (condensed_detachment) R->L }
% 37.05/7.69 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U5, implies(V5, U5)), implies(V5, W6)), implies(implies(V5, U5), implies(implies(W6, U5), implies(V5, U5)))), implies(implies(implies(implies(Y7, Z7), implies(W7, V7)), implies(U7, implies(implies(V7, Y7), implies(W7, Y7)))), implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))))), true, ifeq(is_a_theorem(implies(implies(implies(U5, implies(V5, U5)), implies(V5, W6)), implies(implies(V5, U5), implies(implies(W6, U5), implies(V5, U5))))), true, is_a_theorem(implies(implies(implies(implies(Y7, Z7), implies(W7, V7)), implies(U7, implies(implies(V7, Y7), implies(W7, Y7)))), implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y7, Z7), implies(W7, V7)), implies(U7, implies(implies(V7, Y7), implies(W7, Y7))))), true, is_a_theorem(implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(V5, U5), implies(U5, implies(V5, U5)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.05/7.69 = { by axiom 3 (ic_JLukasiewicz_4) }
% 37.05/7.69 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U5, implies(V5, U5)), implies(V5, W6)), implies(implies(V5, U5), implies(implies(W6, U5), implies(V5, U5))))), true, is_a_theorem(implies(implies(implies(implies(Y7, Z7), implies(W7, V7)), implies(U7, implies(implies(V7, Y7), implies(W7, Y7)))), implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y7, Z7), implies(W7, V7)), implies(U7, implies(implies(V7, Y7), implies(W7, Y7))))), true, is_a_theorem(implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(V5, U5), implies(U5, implies(V5, U5)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.05/7.69 = { by axiom 1 (ifeq_axiom) }
% 37.05/7.69 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U5, implies(V5, U5)), implies(V5, W6)), implies(implies(V5, U5), implies(implies(W6, U5), implies(V5, U5))))), true, is_a_theorem(implies(implies(implies(implies(Y7, Z7), implies(W7, V7)), implies(U7, implies(implies(V7, Y7), implies(W7, Y7)))), implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y7, Z7), implies(W7, V7)), implies(U7, implies(implies(V7, Y7), implies(W7, Y7))))), true, is_a_theorem(implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(V5, U5), implies(U5, implies(V5, U5)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.05/7.70 = { by axiom 3 (ic_JLukasiewicz_4) }
% 37.05/7.70 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y7, Z7), implies(W7, V7)), implies(U7, implies(implies(V7, Y7), implies(W7, Y7)))), implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y7, Z7), implies(W7, V7)), implies(U7, implies(implies(V7, Y7), implies(W7, Y7))))), true, is_a_theorem(implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(V5, U5), implies(U5, implies(V5, U5)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.26/7.70 = { by axiom 1 (ifeq_axiom) }
% 37.26/7.70 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y7, Z7), implies(W7, V7)), implies(U7, implies(implies(V7, Y7), implies(W7, Y7)))), implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5)))))), true, ifeq(is_a_theorem(implies(implies(implies(Y7, Z7), implies(W7, V7)), implies(U7, implies(implies(V7, Y7), implies(W7, Y7))))), true, is_a_theorem(implies(implies(implies(implies(W6, U5), implies(V5, U5)), implies(U5, implies(V5, U5))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(V5, U5), implies(U5, implies(V5, U5)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.26/7.70 = { by axiom 2 (condensed_detachment) }
% 37.26/7.70 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(V5, U5), implies(U5, implies(V5, U5)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.26/7.70 = { by axiom 1 (ifeq_axiom) }
% 37.26/7.70 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(V5, U5), implies(U5, implies(V5, U5))))), true, ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(V5, U5), implies(U5, implies(V5, U5)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.26/7.71 = { by axiom 2 (condensed_detachment) }
% 37.26/7.71 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.26/7.71 = { by axiom 1 (ifeq_axiom) }
% 37.26/7.71 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.26/7.71 = { by axiom 1 (ifeq_axiom) R->L }
% 37.26/7.71 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.26/7.71 = { by axiom 2 (condensed_detachment) R->L }
% 37.26/7.71 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(is_a_theorem(implies(implies(T7, S7), implies(S7, implies(T7, S7)))), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.26/7.72 = { by axiom 1 (ifeq_axiom) R->L }
% 37.26/7.72 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(T7, S7), implies(S7, implies(T7, S7)))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.26/7.72 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 37.26/7.72 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8))))), true, is_a_theorem(implies(implies(T7, S7), implies(S7, implies(T7, S7)))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.26/7.72 = { by axiom 1 (ifeq_axiom) R->L }
% 37.26/7.72 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8))))), true, is_a_theorem(implies(implies(T7, S7), implies(S7, implies(T7, S7)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.26/7.73 = { by axiom 2 (condensed_detachment) R->L }
% 37.26/7.73 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7)))), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(T7, S7), implies(S7, implies(T7, S7)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8))))), true, is_a_theorem(implies(implies(T7, S7), implies(S7, implies(T7, S7)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.26/7.73 = { by axiom 1 (ifeq_axiom) R->L }
% 37.26/7.73 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7)))), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(T7, S7), implies(S7, implies(T7, S7)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8))))), true, is_a_theorem(implies(implies(T7, S7), implies(S7, implies(T7, S7)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.26/7.74 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 37.26/7.74 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(Z9, implies(implies(Y9, T8), implies(X9, T8))))), true, is_a_theorem(implies(implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7)))), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(T7, S7), implies(S7, implies(T7, S7)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8))))), true, is_a_theorem(implies(implies(T7, S7), implies(S7, implies(T7, S7)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.26/7.74 = { by axiom 1 (ifeq_axiom) R->L }
% 37.26/7.74 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(Z9, implies(implies(Y9, T8), implies(X9, T8))))), true, is_a_theorem(implies(implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7)))), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(T7, S7), implies(S7, implies(T7, S7)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8))))), true, is_a_theorem(implies(implies(T7, S7), implies(S7, implies(T7, S7)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.26/7.75 = { by axiom 2 (condensed_detachment) R->L }
% 37.26/7.75 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(S7, implies(U8, S7))), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))))), implies(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(Z9, implies(implies(Y9, T8), implies(X9, T8)))), implies(implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7)))), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(T7, S7), implies(S7, implies(T7, S7)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(S7, implies(U8, S7))), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7)))))), true, is_a_theorem(implies(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(Z9, implies(implies(Y9, T8), implies(X9, T8)))), implies(implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7)))), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(Z9, implies(implies(Y9, T8), implies(X9, T8))))), true, is_a_theorem(implies(implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7)))), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(T7, S7), implies(S7, implies(T7, S7)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8))))), true, is_a_theorem(implies(implies(T7, S7), implies(S7, implies(T7, S7)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.26/7.75 = { by axiom 3 (ic_JLukasiewicz_4) }
% 37.26/7.76 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(S7, implies(U8, S7))), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7)))))), true, is_a_theorem(implies(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(Z9, implies(implies(Y9, T8), implies(X9, T8)))), implies(implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7)))), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(Z9, implies(implies(Y9, T8), implies(X9, T8))))), true, is_a_theorem(implies(implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7)))), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(T7, S7), implies(S7, implies(T7, S7)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8))))), true, is_a_theorem(implies(implies(T7, S7), implies(S7, implies(T7, S7)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.26/7.76 = { by axiom 1 (ifeq_axiom) }
% 37.26/7.76 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(S7, implies(U8, S7))), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7)))))), true, is_a_theorem(implies(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(Z9, implies(implies(Y9, T8), implies(X9, T8)))), implies(implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7)))), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(Z9, implies(implies(Y9, T8), implies(X9, T8))))), true, is_a_theorem(implies(implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7)))), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(T7, S7), implies(S7, implies(T7, S7)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8))))), true, is_a_theorem(implies(implies(T7, S7), implies(S7, implies(T7, S7)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.26/7.77 = { by axiom 3 (ic_JLukasiewicz_4) }
% 37.26/7.77 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(Z9, implies(implies(Y9, T8), implies(X9, T8)))), implies(implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7)))), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(Z9, implies(implies(Y9, T8), implies(X9, T8))))), true, is_a_theorem(implies(implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7)))), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(T7, S7), implies(S7, implies(T7, S7)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8))))), true, is_a_theorem(implies(implies(T7, S7), implies(S7, implies(T7, S7)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.26/7.77 = { by axiom 1 (ifeq_axiom) }
% 37.26/7.77 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(Z9, implies(implies(Y9, T8), implies(X9, T8)))), implies(implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7)))), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))))), true, ifeq(is_a_theorem(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(Z9, implies(implies(Y9, T8), implies(X9, T8))))), true, is_a_theorem(implies(implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7)))), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(T7, S7), implies(S7, implies(T7, S7)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8))))), true, is_a_theorem(implies(implies(T7, S7), implies(S7, implies(T7, S7)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.26/7.78 = { by axiom 2 (condensed_detachment) }
% 37.26/7.78 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8))))), true, is_a_theorem(implies(implies(T7, S7), implies(S7, implies(T7, S7)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.26/7.78 = { by axiom 1 (ifeq_axiom) }
% 37.26/7.78 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8))))), true, is_a_theorem(implies(implies(T7, S7), implies(S7, implies(T7, S7)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.26/7.78 = { by axiom 1 (ifeq_axiom) R->L }
% 37.26/7.78 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8))))), true, is_a_theorem(implies(implies(T7, S7), implies(S7, implies(T7, S7)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.26/7.79 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 37.26/7.79 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W9, V9), implies(U9, T9)), implies(S9, implies(implies(T9, W9), implies(U9, W9))))), true, is_a_theorem(implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8))))), true, is_a_theorem(implies(implies(T7, S7), implies(S7, implies(T7, S7)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.26/7.79 = { by axiom 1 (ifeq_axiom) R->L }
% 37.26/7.79 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W9, V9), implies(U9, T9)), implies(S9, implies(implies(T9, W9), implies(U9, W9))))), true, is_a_theorem(implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8))))), true, is_a_theorem(implies(implies(T7, S7), implies(S7, implies(T7, S7)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.26/7.80 = { by axiom 2 (condensed_detachment) R->L }
% 37.46/7.80 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S7, implies(T7, S7)), implies(T7, U8)), implies(implies(T7, S7), implies(implies(U8, S7), implies(T7, S7)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(S9, implies(implies(T9, W9), implies(U9, W9)))), implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))))), true, ifeq(is_a_theorem(implies(implies(implies(S7, implies(T7, S7)), implies(T7, U8)), implies(implies(T7, S7), implies(implies(U8, S7), implies(T7, S7))))), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(S9, implies(implies(T9, W9), implies(U9, W9)))), implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W9, V9), implies(U9, T9)), implies(S9, implies(implies(T9, W9), implies(U9, W9))))), true, is_a_theorem(implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8))))), true, is_a_theorem(implies(implies(T7, S7), implies(S7, implies(T7, S7)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.46/7.80 = { by axiom 3 (ic_JLukasiewicz_4) }
% 37.46/7.80 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(S7, implies(T7, S7)), implies(T7, U8)), implies(implies(T7, S7), implies(implies(U8, S7), implies(T7, S7))))), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(S9, implies(implies(T9, W9), implies(U9, W9)))), implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W9, V9), implies(U9, T9)), implies(S9, implies(implies(T9, W9), implies(U9, W9))))), true, is_a_theorem(implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8))))), true, is_a_theorem(implies(implies(T7, S7), implies(S7, implies(T7, S7)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.46/7.81 = { by axiom 1 (ifeq_axiom) }
% 37.46/7.81 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S7, implies(T7, S7)), implies(T7, U8)), implies(implies(T7, S7), implies(implies(U8, S7), implies(T7, S7))))), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(S9, implies(implies(T9, W9), implies(U9, W9)))), implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W9, V9), implies(U9, T9)), implies(S9, implies(implies(T9, W9), implies(U9, W9))))), true, is_a_theorem(implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8))))), true, is_a_theorem(implies(implies(T7, S7), implies(S7, implies(T7, S7)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.46/7.81 = { by axiom 3 (ic_JLukasiewicz_4) }
% 37.46/7.81 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(S9, implies(implies(T9, W9), implies(U9, W9)))), implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W9, V9), implies(U9, T9)), implies(S9, implies(implies(T9, W9), implies(U9, W9))))), true, is_a_theorem(implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8))))), true, is_a_theorem(implies(implies(T7, S7), implies(S7, implies(T7, S7)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.46/7.81 = { by axiom 1 (ifeq_axiom) }
% 37.46/7.81 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(S9, implies(implies(T9, W9), implies(U9, W9)))), implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7)))))), true, ifeq(is_a_theorem(implies(implies(implies(W9, V9), implies(U9, T9)), implies(S9, implies(implies(T9, W9), implies(U9, W9))))), true, is_a_theorem(implies(implies(implies(implies(U8, S7), implies(T7, S7)), implies(S7, implies(T7, S7))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8))))), true, is_a_theorem(implies(implies(T7, S7), implies(S7, implies(T7, S7)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.46/7.82 = { by axiom 2 (condensed_detachment) }
% 37.46/7.82 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8))))), true, is_a_theorem(implies(implies(T7, S7), implies(S7, implies(T7, S7)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.46/7.82 = { by axiom 1 (ifeq_axiom) }
% 37.46/7.82 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8)))), implies(implies(T7, S7), implies(S7, implies(T7, S7))))), true, ifeq(is_a_theorem(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(V8, implies(implies(W8, X8), implies(Z8, X8))))), true, is_a_theorem(implies(implies(T7, S7), implies(S7, implies(T7, S7)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.46/7.82 = { by axiom 2 (condensed_detachment) }
% 37.46/7.82 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.46/7.83 = { by axiom 1 (ifeq_axiom) }
% 37.46/7.83 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.46/7.83 = { by axiom 1 (ifeq_axiom) R->L }
% 37.46/7.83 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.46/7.83 = { by axiom 2 (condensed_detachment) R->L }
% 37.46/7.84 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(is_a_theorem(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.46/7.84 = { by axiom 1 (ifeq_axiom) R->L }
% 37.46/7.84 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.46/7.84 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 37.46/7.84 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10))))), true, is_a_theorem(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.46/7.85 = { by axiom 1 (ifeq_axiom) R->L }
% 37.46/7.85 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10))))), true, is_a_theorem(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.46/7.85 = { by axiom 2 (condensed_detachment) R->L }
% 37.46/7.86 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true, is_a_theorem(implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10))))), true, is_a_theorem(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.46/7.86 = { by axiom 1 (ifeq_axiom) R->L }
% 37.46/7.87 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true, is_a_theorem(implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10))))), true, is_a_theorem(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.46/7.87 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 37.46/7.87 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X11, Y11), implies(Z11, W11)), implies(V11, implies(implies(W11, X11), implies(Z11, X11))))), true, is_a_theorem(implies(implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true, is_a_theorem(implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10))))), true, is_a_theorem(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.46/7.88 = { by axiom 1 (ifeq_axiom) R->L }
% 37.46/7.88 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X11, Y11), implies(Z11, W11)), implies(V11, implies(implies(W11, X11), implies(Z11, X11))))), true, is_a_theorem(implies(implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true, is_a_theorem(implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10))))), true, is_a_theorem(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.46/7.89 = { by axiom 2 (condensed_detachment) R->L }
% 37.46/7.89 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(Y10, implies(S10, Y10))), implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))))), implies(implies(implies(implies(X11, Y11), implies(Z11, W11)), implies(V11, implies(implies(W11, X11), implies(Z11, X11)))), implies(implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(Y10, implies(S10, Y10))), implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10)))))), true, is_a_theorem(implies(implies(implies(implies(X11, Y11), implies(Z11, W11)), implies(V11, implies(implies(W11, X11), implies(Z11, X11)))), implies(implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X11, Y11), implies(Z11, W11)), implies(V11, implies(implies(W11, X11), implies(Z11, X11))))), true, is_a_theorem(implies(implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true, is_a_theorem(implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10))))), true, is_a_theorem(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.68/7.90 = { by axiom 3 (ic_JLukasiewicz_4) }
% 37.68/7.90 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(Y10, implies(S10, Y10))), implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10)))))), true, is_a_theorem(implies(implies(implies(implies(X11, Y11), implies(Z11, W11)), implies(V11, implies(implies(W11, X11), implies(Z11, X11)))), implies(implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X11, Y11), implies(Z11, W11)), implies(V11, implies(implies(W11, X11), implies(Z11, X11))))), true, is_a_theorem(implies(implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true, is_a_theorem(implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10))))), true, is_a_theorem(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.68/7.91 = { by axiom 1 (ifeq_axiom) }
% 37.68/7.91 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(Y10, implies(S10, Y10))), implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10)))))), true, is_a_theorem(implies(implies(implies(implies(X11, Y11), implies(Z11, W11)), implies(V11, implies(implies(W11, X11), implies(Z11, X11)))), implies(implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X11, Y11), implies(Z11, W11)), implies(V11, implies(implies(W11, X11), implies(Z11, X11))))), true, is_a_theorem(implies(implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true, is_a_theorem(implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10))))), true, is_a_theorem(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.68/7.91 = { by axiom 3 (ic_JLukasiewicz_4) }
% 37.68/7.92 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X11, Y11), implies(Z11, W11)), implies(V11, implies(implies(W11, X11), implies(Z11, X11)))), implies(implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X11, Y11), implies(Z11, W11)), implies(V11, implies(implies(W11, X11), implies(Z11, X11))))), true, is_a_theorem(implies(implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true, is_a_theorem(implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10))))), true, is_a_theorem(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.68/7.92 = { by axiom 1 (ifeq_axiom) }
% 37.68/7.93 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X11, Y11), implies(Z11, W11)), implies(V11, implies(implies(W11, X11), implies(Z11, X11)))), implies(implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))))), true, ifeq(is_a_theorem(implies(implies(implies(X11, Y11), implies(Z11, W11)), implies(V11, implies(implies(W11, X11), implies(Z11, X11))))), true, is_a_theorem(implies(implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true, is_a_theorem(implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10))))), true, is_a_theorem(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.68/7.93 = { by axiom 2 (condensed_detachment) }
% 37.68/7.93 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true, is_a_theorem(implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10))))), true, is_a_theorem(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.68/7.93 = { by axiom 1 (ifeq_axiom) }
% 37.68/7.94 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true, is_a_theorem(implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10))))), true, is_a_theorem(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.68/7.94 = { by axiom 1 (ifeq_axiom) R->L }
% 37.68/7.94 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true), true, is_a_theorem(implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10))))), true, is_a_theorem(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.68/7.95 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 37.68/7.95 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U11, T11), implies(S11, X12)), implies(Y12, implies(implies(X12, U11), implies(S11, U11))))), true, is_a_theorem(implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true), true, is_a_theorem(implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10))))), true, is_a_theorem(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.68/7.95 = { by axiom 1 (ifeq_axiom) R->L }
% 37.68/7.96 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U11, T11), implies(S11, X12)), implies(Y12, implies(implies(X12, U11), implies(S11, U11))))), true, is_a_theorem(implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10))))), true, is_a_theorem(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.68/7.96 = { by axiom 2 (condensed_detachment) R->L }
% 37.68/7.96 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y10, implies(X10, Y10)), implies(X10, S10)), implies(implies(X10, Y10), implies(implies(S10, Y10), implies(X10, Y10)))), implies(implies(implies(implies(U11, T11), implies(S11, X12)), implies(Y12, implies(implies(X12, U11), implies(S11, U11)))), implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))))), true, ifeq(is_a_theorem(implies(implies(implies(Y10, implies(X10, Y10)), implies(X10, S10)), implies(implies(X10, Y10), implies(implies(S10, Y10), implies(X10, Y10))))), true, is_a_theorem(implies(implies(implies(implies(U11, T11), implies(S11, X12)), implies(Y12, implies(implies(X12, U11), implies(S11, U11)))), implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U11, T11), implies(S11, X12)), implies(Y12, implies(implies(X12, U11), implies(S11, U11))))), true, is_a_theorem(implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10))))), true, is_a_theorem(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.68/7.97 = { by axiom 3 (ic_JLukasiewicz_4) }
% 37.68/7.97 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y10, implies(X10, Y10)), implies(X10, S10)), implies(implies(X10, Y10), implies(implies(S10, Y10), implies(X10, Y10))))), true, is_a_theorem(implies(implies(implies(implies(U11, T11), implies(S11, X12)), implies(Y12, implies(implies(X12, U11), implies(S11, U11)))), implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U11, T11), implies(S11, X12)), implies(Y12, implies(implies(X12, U11), implies(S11, U11))))), true, is_a_theorem(implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10))))), true, is_a_theorem(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.68/7.98 = { by axiom 1 (ifeq_axiom) }
% 37.68/7.98 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y10, implies(X10, Y10)), implies(X10, S10)), implies(implies(X10, Y10), implies(implies(S10, Y10), implies(X10, Y10))))), true, is_a_theorem(implies(implies(implies(implies(U11, T11), implies(S11, X12)), implies(Y12, implies(implies(X12, U11), implies(S11, U11)))), implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U11, T11), implies(S11, X12)), implies(Y12, implies(implies(X12, U11), implies(S11, U11))))), true, is_a_theorem(implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10))))), true, is_a_theorem(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.68/7.98 = { by axiom 3 (ic_JLukasiewicz_4) }
% 37.68/7.99 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U11, T11), implies(S11, X12)), implies(Y12, implies(implies(X12, U11), implies(S11, U11)))), implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U11, T11), implies(S11, X12)), implies(Y12, implies(implies(X12, U11), implies(S11, U11))))), true, is_a_theorem(implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10))))), true, is_a_theorem(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.68/7.99 = { by axiom 1 (ifeq_axiom) }
% 37.68/7.99 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U11, T11), implies(S11, X12)), implies(Y12, implies(implies(X12, U11), implies(S11, U11)))), implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))))), true, ifeq(is_a_theorem(implies(implies(implies(U11, T11), implies(S11, X12)), implies(Y12, implies(implies(X12, U11), implies(S11, U11))))), true, is_a_theorem(implies(implies(implies(implies(S10, Y10), implies(X10, Y10)), implies(Y10, implies(X10, Y10))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10))))), true, is_a_theorem(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.68/7.99 = { by axiom 2 (condensed_detachment) }
% 37.68/8.00 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10))))), true, is_a_theorem(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.68/8.00 = { by axiom 1 (ifeq_axiom) }
% 37.68/8.00 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10)))), implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))))), true, ifeq(is_a_theorem(implies(implies(implies(Z10, W10), implies(V10, U10)), implies(T10, implies(implies(U10, Z10), implies(V10, Z10))))), true, is_a_theorem(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.68/8.00 = { by axiom 2 (condensed_detachment) }
% 37.68/8.00 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.68/8.01 = { by axiom 1 (ifeq_axiom) }
% 37.68/8.01 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.68/8.01 = { by axiom 1 (ifeq_axiom) R->L }
% 37.68/8.02 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.68/8.02 = { by axiom 2 (condensed_detachment) R->L }
% 37.68/8.03 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(is_a_theorem(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.95/8.03 = { by axiom 1 (ifeq_axiom) R->L }
% 37.95/8.03 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.95/8.04 = { by axiom 2 (condensed_detachment) R->L }
% 37.95/8.05 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S12, X13), implies(Y13, Z13)), implies(W13, implies(implies(Z13, S12), implies(Y13, S12)))), implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, ifeq(is_a_theorem(implies(implies(implies(S12, X13), implies(Y13, Z13)), implies(W13, implies(implies(Z13, S12), implies(Y13, S12))))), true, is_a_theorem(implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.95/8.05 = { by axiom 1 (ifeq_axiom) R->L }
% 37.95/8.06 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S12, X13), implies(Y13, Z13)), implies(W13, implies(implies(Z13, S12), implies(Y13, S12)))), implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S12, X13), implies(Y13, Z13)), implies(W13, implies(implies(Z13, S12), implies(Y13, S12))))), true, is_a_theorem(implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.95/8.07 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 37.95/8.07 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), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), V13)), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(implies(S12, X13), implies(Y13, Z13)), implies(W13, implies(implies(Z13, S12), implies(Y13, S12)))), implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S12, X13), implies(Y13, Z13)), implies(W13, implies(implies(Z13, S12), implies(Y13, S12))))), true, is_a_theorem(implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.95/8.08 = { by axiom 1 (ifeq_axiom) R->L }
% 37.95/8.08 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), V13)), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(implies(S12, X13), implies(Y13, Z13)), implies(W13, implies(implies(Z13, S12), implies(Y13, S12)))), implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S12, X13), implies(Y13, Z13)), implies(W13, implies(implies(Z13, S12), implies(Y13, S12))))), true, is_a_theorem(implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.95/8.09 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 37.95/8.10 ifeq(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), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), V13)), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(S12, X13), implies(Y13, Z13)), implies(W13, implies(implies(Z13, S12), implies(Y13, S12)))), implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), V13)), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(implies(S12, X13), implies(Y13, Z13)), implies(W13, implies(implies(Z13, S12), implies(Y13, S12)))), implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S12, X13), implies(Y13, Z13)), implies(W13, implies(implies(Z13, S12), implies(Y13, S12))))), true, is_a_theorem(implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.95/8.10 = { by axiom 2 (condensed_detachment) }
% 37.95/8.10 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(S12, X13), implies(Y13, Z13)), implies(W13, implies(implies(Z13, S12), implies(Y13, S12))))), true, is_a_theorem(implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.95/8.11 = { by axiom 1 (ifeq_axiom) }
% 37.95/8.12 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S12, X13), implies(Y13, Z13)), implies(W13, implies(implies(Z13, S12), implies(Y13, S12))))), true, is_a_theorem(implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 37.95/8.12 = { by axiom 3 (ic_JLukasiewicz_4) }
% 37.95/8.13 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.16/8.13 = { by axiom 1 (ifeq_axiom) }
% 38.16/8.14 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.16/8.15 = { by axiom 1 (ifeq_axiom) R->L }
% 38.16/8.15 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.16/8.16 = { by axiom 2 (condensed_detachment) R->L }
% 38.16/8.17 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U13, T13), implies(S13, X14)), implies(Y14, implies(implies(X14, U13), implies(S13, U13)))), implies(implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))))), true, ifeq(is_a_theorem(implies(implies(implies(U13, T13), implies(S13, X14)), implies(Y14, implies(implies(X14, U13), implies(S13, U13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.16/8.18 = { by axiom 1 (ifeq_axiom) R->L }
% 38.16/8.19 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U13, T13), implies(S13, X14)), implies(Y14, implies(implies(X14, U13), implies(S13, U13)))), implies(implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U13, T13), implies(S13, X14)), implies(Y14, implies(implies(X14, U13), implies(S13, U13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.28/8.20 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 38.28/8.23 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(a, b), b), implies(V13, implies(implies(a, b), b)))), implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(U13, T13), implies(S13, X14)), implies(Y14, implies(implies(X14, U13), implies(S13, U13)))), implies(implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U13, T13), implies(S13, X14)), implies(Y14, implies(implies(X14, U13), implies(S13, U13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.28/8.23 = { by axiom 1 (ifeq_axiom) R->L }
% 38.28/8.24 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(a, b), b), implies(V13, implies(implies(a, b), b)))), implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(U13, T13), implies(S13, X14)), implies(Y14, implies(implies(X14, U13), implies(S13, U13)))), implies(implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U13, T13), implies(S13, X14)), implies(Y14, implies(implies(X14, U13), implies(S13, U13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.28/8.24 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 38.28/8.26 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(a, b), b), implies(V13, implies(implies(a, b), b)))), implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), implies(implies(implies(implies(U13, T13), implies(S13, X14)), implies(Y14, implies(implies(X14, U13), implies(S13, U13)))), implies(implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(a, b), b), implies(V13, implies(implies(a, b), b)))), implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(U13, T13), implies(S13, X14)), implies(Y14, implies(implies(X14, U13), implies(S13, U13)))), implies(implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U13, T13), implies(S13, X14)), implies(Y14, implies(implies(X14, U13), implies(S13, U13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.28/8.26 = { by axiom 2 (condensed_detachment) }
% 38.28/8.26 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U13, T13), implies(S13, X14)), implies(Y14, implies(implies(X14, U13), implies(S13, U13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.28/8.27 = { by axiom 1 (ifeq_axiom) }
% 38.28/8.27 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U13, T13), implies(S13, X14)), implies(Y14, implies(implies(X14, U13), implies(S13, U13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.28/8.28 = { by axiom 3 (ic_JLukasiewicz_4) }
% 38.28/8.28 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.28/8.28 = { by axiom 1 (ifeq_axiom) }
% 38.28/8.29 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(V13, implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.28/8.29 = { by axiom 2 (condensed_detachment) }
% 38.28/8.29 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.28/8.30 = { by axiom 1 (ifeq_axiom) }
% 38.28/8.30 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.49/8.30 = { by axiom 3 (ic_JLukasiewicz_4) }
% 38.49/8.30 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(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.49/8.30 = { by axiom 1 (ifeq_axiom) }
% 38.49/8.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.49/8.31 = { by axiom 1 (ifeq_axiom) R->L }
% 38.49/8.31 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(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.49/8.31 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 38.49/8.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), b), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(X10, Y10), implies(Y10, implies(X10, Y10))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.49/8.32 = { by axiom 2 (condensed_detachment) }
% 38.49/8.32 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.49/8.32 = { by axiom 1 (ifeq_axiom) }
% 38.49/8.32 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.49/8.32 = { by axiom 1 (ifeq_axiom) R->L }
% 38.49/8.33 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.49/8.33 = { by axiom 2 (condensed_detachment) R->L }
% 38.49/8.33 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z14, W14), implies(V14, U14)), implies(T14, implies(implies(U14, Z14), implies(V14, Z14)))), implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, ifeq(is_a_theorem(implies(implies(implies(Z14, W14), implies(V14, U14)), implies(T14, implies(implies(U14, Z14), implies(V14, Z14))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.49/8.34 = { by axiom 1 (ifeq_axiom) R->L }
% 38.49/8.34 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z14, W14), implies(V14, U14)), implies(T14, implies(implies(U14, Z14), implies(V14, Z14)))), implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z14, W14), implies(V14, U14)), implies(T14, implies(implies(U14, Z14), implies(V14, Z14))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.49/8.34 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 38.49/8.35 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(implies(Z14, W14), implies(V14, U14)), implies(T14, implies(implies(U14, Z14), implies(V14, Z14)))), implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z14, W14), implies(V14, U14)), implies(T14, implies(implies(U14, Z14), implies(V14, Z14))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.49/8.35 = { by axiom 1 (ifeq_axiom) R->L }
% 38.49/8.35 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(implies(Z14, W14), implies(V14, U14)), implies(T14, implies(implies(U14, Z14), implies(V14, Z14)))), implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z14, W14), implies(V14, U14)), implies(T14, implies(implies(U14, Z14), implies(V14, Z14))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.49/8.35 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 38.49/8.36 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(Z14, W14), implies(V14, U14)), implies(T14, implies(implies(U14, Z14), implies(V14, Z14)))), implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(implies(Z14, W14), implies(V14, U14)), implies(T14, implies(implies(U14, Z14), implies(V14, Z14)))), implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z14, W14), implies(V14, U14)), implies(T14, implies(implies(U14, Z14), implies(V14, Z14))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.49/8.36 = { by axiom 2 (condensed_detachment) }
% 38.49/8.36 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Z14, W14), implies(V14, U14)), implies(T14, implies(implies(U14, Z14), implies(V14, Z14))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.49/8.36 = { by axiom 1 (ifeq_axiom) }
% 38.49/8.37 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z14, W14), implies(V14, U14)), implies(T14, implies(implies(U14, Z14), implies(V14, Z14))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.49/8.37 = { by axiom 3 (ic_JLukasiewicz_4) }
% 38.49/8.37 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.49/8.37 = { by axiom 1 (ifeq_axiom) }
% 38.49/8.37 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(T7, S7), implies(S7, implies(T7, S7))), implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.49/8.37 = { by axiom 2 (condensed_detachment) }
% 38.49/8.37 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.49/8.37 = { by axiom 1 (ifeq_axiom) }
% 38.49/8.38 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.49/8.38 = { by axiom 1 (ifeq_axiom) R->L }
% 38.49/8.38 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.49/8.38 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 38.49/8.38 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), b), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(V5, U5), implies(U5, implies(V5, U5))), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.49/8.38 = { by axiom 2 (condensed_detachment) }
% 38.49/8.38 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.49/8.38 = { by axiom 1 (ifeq_axiom) }
% 38.49/8.38 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.49/8.38 = { by axiom 1 (ifeq_axiom) R->L }
% 38.49/8.38 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.49/8.38 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 38.49/8.38 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b))), implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, b)))), true, is_a_theorem(implies(implies(implies(Z3, W3), implies(W3, implies(Z3, W3))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.49/8.38 = { by axiom 2 (condensed_detachment) }
% 38.49/8.38 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.49/8.38 = { by axiom 1 (ifeq_axiom) }
% 38.49/8.39 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.49/8.39 = { by axiom 1 (ifeq_axiom) R->L }
% 38.49/8.39 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.49/8.39 = { by axiom 2 (condensed_detachment) R->L }
% 38.49/8.39 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(is_a_theorem(implies(implies(S14, X15), implies(X15, implies(S14, X15)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.49/8.39 = { by axiom 1 (ifeq_axiom) R->L }
% 38.49/8.39 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(S14, X15), implies(X15, implies(S14, X15)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.49/8.39 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 38.49/8.39 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15))))), true, is_a_theorem(implies(implies(S14, X15), implies(X15, implies(S14, X15)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.49/8.40 = { by axiom 1 (ifeq_axiom) R->L }
% 38.49/8.40 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15))))), true, is_a_theorem(implies(implies(S14, X15), implies(X15, implies(S14, X15)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.49/8.40 = { by axiom 2 (condensed_detachment) R->L }
% 38.70/8.40 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15)))), implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(S14, X15), implies(X15, implies(S14, X15)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true, is_a_theorem(implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15))))), true, is_a_theorem(implies(implies(S14, X15), implies(X15, implies(S14, X15)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.70/8.40 = { by axiom 1 (ifeq_axiom) R->L }
% 38.70/8.40 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15)))), implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(S14, X15), implies(X15, implies(S14, X15)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true, is_a_theorem(implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15))))), true, is_a_theorem(implies(implies(S14, X15), implies(X15, implies(S14, X15)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.70/8.41 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 38.70/8.41 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(W16, implies(implies(Z16, S15), implies(Y16, S15))))), true, is_a_theorem(implies(implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15)))), implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(S14, X15), implies(X15, implies(S14, X15)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true, is_a_theorem(implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15))))), true, is_a_theorem(implies(implies(S14, X15), implies(X15, implies(S14, X15)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.70/8.41 = { by axiom 1 (ifeq_axiom) R->L }
% 38.70/8.41 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(W16, implies(implies(Z16, S15), implies(Y16, S15))))), true, is_a_theorem(implies(implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15)))), implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(S14, X15), implies(X15, implies(S14, X15)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true, is_a_theorem(implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15))))), true, is_a_theorem(implies(implies(S14, X15), implies(X15, implies(S14, X15)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.70/8.42 = { by axiom 2 (condensed_detachment) R->L }
% 38.70/8.42 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(X15, implies(T15, X15))), implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))))), implies(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(W16, implies(implies(Z16, S15), implies(Y16, S15)))), implies(implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15)))), implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(S14, X15), implies(X15, implies(S14, X15)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(X15, implies(T15, X15))), implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15)))))), true, is_a_theorem(implies(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(W16, implies(implies(Z16, S15), implies(Y16, S15)))), implies(implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15)))), implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(W16, implies(implies(Z16, S15), implies(Y16, S15))))), true, is_a_theorem(implies(implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15)))), implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(S14, X15), implies(X15, implies(S14, X15)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true, is_a_theorem(implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15))))), true, is_a_theorem(implies(implies(S14, X15), implies(X15, implies(S14, X15)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.70/8.42 = { by axiom 3 (ic_JLukasiewicz_4) }
% 38.70/8.42 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(X15, implies(T15, X15))), implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15)))))), true, is_a_theorem(implies(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(W16, implies(implies(Z16, S15), implies(Y16, S15)))), implies(implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15)))), implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(W16, implies(implies(Z16, S15), implies(Y16, S15))))), true, is_a_theorem(implies(implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15)))), implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(S14, X15), implies(X15, implies(S14, X15)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true, is_a_theorem(implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15))))), true, is_a_theorem(implies(implies(S14, X15), implies(X15, implies(S14, X15)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.70/8.43 = { by axiom 1 (ifeq_axiom) }
% 38.70/8.43 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(X15, implies(T15, X15))), implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15)))))), true, is_a_theorem(implies(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(W16, implies(implies(Z16, S15), implies(Y16, S15)))), implies(implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15)))), implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(W16, implies(implies(Z16, S15), implies(Y16, S15))))), true, is_a_theorem(implies(implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15)))), implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(S14, X15), implies(X15, implies(S14, X15)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true, is_a_theorem(implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15))))), true, is_a_theorem(implies(implies(S14, X15), implies(X15, implies(S14, X15)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.70/8.43 = { by axiom 3 (ic_JLukasiewicz_4) }
% 38.70/8.43 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(W16, implies(implies(Z16, S15), implies(Y16, S15)))), implies(implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15)))), implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(W16, implies(implies(Z16, S15), implies(Y16, S15))))), true, is_a_theorem(implies(implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15)))), implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(S14, X15), implies(X15, implies(S14, X15)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true, is_a_theorem(implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15))))), true, is_a_theorem(implies(implies(S14, X15), implies(X15, implies(S14, X15)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.70/8.43 = { by axiom 1 (ifeq_axiom) }
% 38.70/8.44 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(W16, implies(implies(Z16, S15), implies(Y16, S15)))), implies(implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15)))), implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))))), true, ifeq(is_a_theorem(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(W16, implies(implies(Z16, S15), implies(Y16, S15))))), true, is_a_theorem(implies(implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15)))), implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(S14, X15), implies(X15, implies(S14, X15)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true, is_a_theorem(implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15))))), true, is_a_theorem(implies(implies(S14, X15), implies(X15, implies(S14, X15)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.70/8.44 = { by axiom 2 (condensed_detachment) }
% 38.70/8.44 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true, is_a_theorem(implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15))))), true, is_a_theorem(implies(implies(S14, X15), implies(X15, implies(S14, X15)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.70/8.44 = { by axiom 1 (ifeq_axiom) }
% 38.70/8.44 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true, is_a_theorem(implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15))))), true, is_a_theorem(implies(implies(S14, X15), implies(X15, implies(S14, X15)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.70/8.44 = { by axiom 1 (ifeq_axiom) R->L }
% 38.70/8.45 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true), true, is_a_theorem(implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15))))), true, is_a_theorem(implies(implies(S14, X15), implies(X15, implies(S14, X15)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.70/8.45 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 38.70/8.45 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V16, U16), implies(T16, S16)), implies(X17, implies(implies(S16, V16), implies(T16, V16))))), true, is_a_theorem(implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true), true, is_a_theorem(implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15))))), true, is_a_theorem(implies(implies(S14, X15), implies(X15, implies(S14, X15)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.70/8.45 = { by axiom 1 (ifeq_axiom) R->L }
% 38.70/8.45 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V16, U16), implies(T16, S16)), implies(X17, implies(implies(S16, V16), implies(T16, V16))))), true, is_a_theorem(implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15))))), true, is_a_theorem(implies(implies(S14, X15), implies(X15, implies(S14, X15)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.70/8.45 = { by axiom 2 (condensed_detachment) R->L }
% 38.70/8.46 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X15, implies(S14, X15)), implies(S14, T15)), implies(implies(S14, X15), implies(implies(T15, X15), implies(S14, X15)))), implies(implies(implies(implies(V16, U16), implies(T16, S16)), implies(X17, implies(implies(S16, V16), implies(T16, V16)))), implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))))), true, ifeq(is_a_theorem(implies(implies(implies(X15, implies(S14, X15)), implies(S14, T15)), implies(implies(S14, X15), implies(implies(T15, X15), implies(S14, X15))))), true, is_a_theorem(implies(implies(implies(implies(V16, U16), implies(T16, S16)), implies(X17, implies(implies(S16, V16), implies(T16, V16)))), implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V16, U16), implies(T16, S16)), implies(X17, implies(implies(S16, V16), implies(T16, V16))))), true, is_a_theorem(implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15))))), true, is_a_theorem(implies(implies(S14, X15), implies(X15, implies(S14, X15)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.70/8.46 = { by axiom 3 (ic_JLukasiewicz_4) }
% 38.70/8.46 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X15, implies(S14, X15)), implies(S14, T15)), implies(implies(S14, X15), implies(implies(T15, X15), implies(S14, X15))))), true, is_a_theorem(implies(implies(implies(implies(V16, U16), implies(T16, S16)), implies(X17, implies(implies(S16, V16), implies(T16, V16)))), implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V16, U16), implies(T16, S16)), implies(X17, implies(implies(S16, V16), implies(T16, V16))))), true, is_a_theorem(implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15))))), true, is_a_theorem(implies(implies(S14, X15), implies(X15, implies(S14, X15)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.70/8.46 = { by axiom 1 (ifeq_axiom) }
% 38.70/8.46 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X15, implies(S14, X15)), implies(S14, T15)), implies(implies(S14, X15), implies(implies(T15, X15), implies(S14, X15))))), true, is_a_theorem(implies(implies(implies(implies(V16, U16), implies(T16, S16)), implies(X17, implies(implies(S16, V16), implies(T16, V16)))), implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V16, U16), implies(T16, S16)), implies(X17, implies(implies(S16, V16), implies(T16, V16))))), true, is_a_theorem(implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15))))), true, is_a_theorem(implies(implies(S14, X15), implies(X15, implies(S14, X15)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.70/8.46 = { by axiom 3 (ic_JLukasiewicz_4) }
% 38.70/8.47 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V16, U16), implies(T16, S16)), implies(X17, implies(implies(S16, V16), implies(T16, V16)))), implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V16, U16), implies(T16, S16)), implies(X17, implies(implies(S16, V16), implies(T16, V16))))), true, is_a_theorem(implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15))))), true, is_a_theorem(implies(implies(S14, X15), implies(X15, implies(S14, X15)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.70/8.47 = { by axiom 1 (ifeq_axiom) }
% 38.70/8.47 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V16, U16), implies(T16, S16)), implies(X17, implies(implies(S16, V16), implies(T16, V16)))), implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15)))))), true, ifeq(is_a_theorem(implies(implies(implies(V16, U16), implies(T16, S16)), implies(X17, implies(implies(S16, V16), implies(T16, V16))))), true, is_a_theorem(implies(implies(implies(implies(T15, X15), implies(S14, X15)), implies(X15, implies(S14, X15))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15))))), true, is_a_theorem(implies(implies(S14, X15), implies(X15, implies(S14, X15)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.70/8.47 = { by axiom 2 (condensed_detachment) }
% 38.70/8.47 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15))))), true, is_a_theorem(implies(implies(S14, X15), implies(X15, implies(S14, X15)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.70/8.47 = { by axiom 1 (ifeq_axiom) }
% 38.70/8.47 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15)))), implies(implies(S14, X15), implies(X15, implies(S14, X15))))), true, ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(W15, V15)), implies(U15, implies(implies(V15, Y15), implies(W15, Y15))))), true, is_a_theorem(implies(implies(S14, X15), implies(X15, implies(S14, X15)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.70/8.47 = { by axiom 2 (condensed_detachment) }
% 38.70/8.48 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.70/8.48 = { by axiom 1 (ifeq_axiom) }
% 38.70/8.48 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.70/8.48 = { by axiom 1 (ifeq_axiom) R->L }
% 38.70/8.48 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.70/8.48 = { by axiom 2 (condensed_detachment) R->L }
% 38.70/8.48 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true, ifeq(is_a_theorem(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.70/8.48 = { by axiom 1 (ifeq_axiom) R->L }
% 38.70/8.49 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.70/8.49 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 38.70/8.49 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17))))), true, is_a_theorem(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.70/8.49 = { by axiom 1 (ifeq_axiom) R->L }
% 38.70/8.49 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17))))), true, is_a_theorem(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.70/8.50 = { by axiom 2 (condensed_detachment) R->L }
% 38.91/8.50 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true, is_a_theorem(implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17))))), true, is_a_theorem(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.91/8.50 = { by axiom 1 (ifeq_axiom) R->L }
% 38.91/8.50 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true, is_a_theorem(implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17))))), true, is_a_theorem(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.91/8.51 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 38.91/8.51 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y18, Z18), implies(W18, V18)), implies(U18, implies(implies(V18, Y18), implies(W18, Y18))))), true, is_a_theorem(implies(implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true, is_a_theorem(implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17))))), true, is_a_theorem(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.91/8.51 = { by axiom 1 (ifeq_axiom) R->L }
% 38.91/8.52 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y18, Z18), implies(W18, V18)), implies(U18, implies(implies(V18, Y18), implies(W18, Y18))))), true, is_a_theorem(implies(implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true, is_a_theorem(implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17))))), true, is_a_theorem(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.91/8.52 = { by axiom 2 (condensed_detachment) R->L }
% 38.91/8.52 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(Z17, implies(X18, Z17))), implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))))), implies(implies(implies(implies(Y18, Z18), implies(W18, V18)), implies(U18, implies(implies(V18, Y18), implies(W18, Y18)))), implies(implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(Z17, implies(X18, Z17))), implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17)))))), true, is_a_theorem(implies(implies(implies(implies(Y18, Z18), implies(W18, V18)), implies(U18, implies(implies(V18, Y18), implies(W18, Y18)))), implies(implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y18, Z18), implies(W18, V18)), implies(U18, implies(implies(V18, Y18), implies(W18, Y18))))), true, is_a_theorem(implies(implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true, is_a_theorem(implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17))))), true, is_a_theorem(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.91/8.53 = { by axiom 3 (ic_JLukasiewicz_4) }
% 38.91/8.53 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(Z17, implies(X18, Z17))), implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17)))))), true, is_a_theorem(implies(implies(implies(implies(Y18, Z18), implies(W18, V18)), implies(U18, implies(implies(V18, Y18), implies(W18, Y18)))), implies(implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y18, Z18), implies(W18, V18)), implies(U18, implies(implies(V18, Y18), implies(W18, Y18))))), true, is_a_theorem(implies(implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true, is_a_theorem(implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17))))), true, is_a_theorem(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.91/8.53 = { by axiom 1 (ifeq_axiom) }
% 38.91/8.54 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(Z17, implies(X18, Z17))), implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17)))))), true, is_a_theorem(implies(implies(implies(implies(Y18, Z18), implies(W18, V18)), implies(U18, implies(implies(V18, Y18), implies(W18, Y18)))), implies(implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y18, Z18), implies(W18, V18)), implies(U18, implies(implies(V18, Y18), implies(W18, Y18))))), true, is_a_theorem(implies(implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true, is_a_theorem(implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17))))), true, is_a_theorem(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.91/8.54 = { by axiom 3 (ic_JLukasiewicz_4) }
% 38.91/8.54 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y18, Z18), implies(W18, V18)), implies(U18, implies(implies(V18, Y18), implies(W18, Y18)))), implies(implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y18, Z18), implies(W18, V18)), implies(U18, implies(implies(V18, Y18), implies(W18, Y18))))), true, is_a_theorem(implies(implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true, is_a_theorem(implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17))))), true, is_a_theorem(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.91/8.54 = { by axiom 1 (ifeq_axiom) }
% 38.91/8.55 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y18, Z18), implies(W18, V18)), implies(U18, implies(implies(V18, Y18), implies(W18, Y18)))), implies(implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))))), true, ifeq(is_a_theorem(implies(implies(implies(Y18, Z18), implies(W18, V18)), implies(U18, implies(implies(V18, Y18), implies(W18, Y18))))), true, is_a_theorem(implies(implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true, is_a_theorem(implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17))))), true, is_a_theorem(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.91/8.55 = { by axiom 2 (condensed_detachment) }
% 38.91/8.55 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true, is_a_theorem(implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17))))), true, is_a_theorem(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.91/8.55 = { by axiom 1 (ifeq_axiom) }
% 38.91/8.55 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true, is_a_theorem(implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17))))), true, is_a_theorem(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.91/8.56 = { by axiom 1 (ifeq_axiom) R->L }
% 38.91/8.56 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true), true, is_a_theorem(implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17))))), true, is_a_theorem(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.91/8.56 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 38.91/8.56 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T18, S18), implies(X19, Y19)), implies(Z19, implies(implies(Y19, T18), implies(X19, T18))))), true, is_a_theorem(implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true), true, is_a_theorem(implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17))))), true, is_a_theorem(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.91/8.57 = { by axiom 1 (ifeq_axiom) R->L }
% 38.91/8.57 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T18, S18), implies(X19, Y19)), implies(Z19, implies(implies(Y19, T18), implies(X19, T18))))), true, is_a_theorem(implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17))))), true, is_a_theorem(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.91/8.57 = { by axiom 2 (condensed_detachment) R->L }
% 38.91/8.57 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z17, implies(Y17, Z17)), implies(Y17, X18)), implies(implies(Y17, Z17), implies(implies(X18, Z17), implies(Y17, Z17)))), implies(implies(implies(implies(T18, S18), implies(X19, Y19)), implies(Z19, implies(implies(Y19, T18), implies(X19, T18)))), implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))))), true, ifeq(is_a_theorem(implies(implies(implies(Z17, implies(Y17, Z17)), implies(Y17, X18)), implies(implies(Y17, Z17), implies(implies(X18, Z17), implies(Y17, Z17))))), true, is_a_theorem(implies(implies(implies(implies(T18, S18), implies(X19, Y19)), implies(Z19, implies(implies(Y19, T18), implies(X19, T18)))), implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T18, S18), implies(X19, Y19)), implies(Z19, implies(implies(Y19, T18), implies(X19, T18))))), true, is_a_theorem(implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17))))), true, is_a_theorem(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.91/8.58 = { by axiom 3 (ic_JLukasiewicz_4) }
% 38.91/8.58 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Z17, implies(Y17, Z17)), implies(Y17, X18)), implies(implies(Y17, Z17), implies(implies(X18, Z17), implies(Y17, Z17))))), true, is_a_theorem(implies(implies(implies(implies(T18, S18), implies(X19, Y19)), implies(Z19, implies(implies(Y19, T18), implies(X19, T18)))), implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T18, S18), implies(X19, Y19)), implies(Z19, implies(implies(Y19, T18), implies(X19, T18))))), true, is_a_theorem(implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17))))), true, is_a_theorem(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.91/8.58 = { by axiom 1 (ifeq_axiom) }
% 38.91/8.58 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z17, implies(Y17, Z17)), implies(Y17, X18)), implies(implies(Y17, Z17), implies(implies(X18, Z17), implies(Y17, Z17))))), true, is_a_theorem(implies(implies(implies(implies(T18, S18), implies(X19, Y19)), implies(Z19, implies(implies(Y19, T18), implies(X19, T18)))), implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T18, S18), implies(X19, Y19)), implies(Z19, implies(implies(Y19, T18), implies(X19, T18))))), true, is_a_theorem(implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17))))), true, is_a_theorem(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.91/8.59 = { by axiom 3 (ic_JLukasiewicz_4) }
% 38.91/8.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T18, S18), implies(X19, Y19)), implies(Z19, implies(implies(Y19, T18), implies(X19, T18)))), implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T18, S18), implies(X19, Y19)), implies(Z19, implies(implies(Y19, T18), implies(X19, T18))))), true, is_a_theorem(implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17))))), true, is_a_theorem(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.91/8.59 = { by axiom 1 (ifeq_axiom) }
% 38.91/8.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T18, S18), implies(X19, Y19)), implies(Z19, implies(implies(Y19, T18), implies(X19, T18)))), implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))))), true, ifeq(is_a_theorem(implies(implies(implies(T18, S18), implies(X19, Y19)), implies(Z19, implies(implies(Y19, T18), implies(X19, T18))))), true, is_a_theorem(implies(implies(implies(implies(X18, Z17), implies(Y17, Z17)), implies(Z17, implies(Y17, Z17))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17))))), true, is_a_theorem(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.91/8.59 = { by axiom 2 (condensed_detachment) }
% 38.91/8.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17))))), true, is_a_theorem(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 38.91/8.60 = { by axiom 1 (ifeq_axiom) }
% 39.11/8.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17)))), implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))))), true, ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(U17, T17)), implies(S17, implies(implies(T17, W17), implies(U17, W17))))), true, is_a_theorem(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.11/8.60 = { by axiom 2 (condensed_detachment) }
% 39.11/8.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.11/8.60 = { by axiom 1 (ifeq_axiom) }
% 39.11/8.61 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.11/8.61 = { by axiom 1 (ifeq_axiom) R->L }
% 39.11/8.61 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.11/8.61 = { by axiom 2 (condensed_detachment) R->L }
% 39.11/8.61 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(is_a_theorem(implies(implies(W19, V19), implies(V19, implies(W19, V19)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.11/8.62 = { by axiom 1 (ifeq_axiom) R->L }
% 39.11/8.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(W19, V19)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.11/8.62 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 39.11/8.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(W19, V19)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.11/8.63 = { by axiom 1 (ifeq_axiom) R->L }
% 39.11/8.63 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(W19, V19)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.11/8.63 = { by axiom 2 (condensed_detachment) R->L }
% 39.11/8.64 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19)))), implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(W19, V19), implies(V19, implies(W19, V19)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true, is_a_theorem(implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(W19, V19)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.11/8.64 = { by axiom 1 (ifeq_axiom) R->L }
% 39.11/8.64 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19)))), implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(W19, V19), implies(V19, implies(W19, V19)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true, is_a_theorem(implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(W19, V19)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.11/8.65 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 39.11/8.65 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W20, V20), implies(U20, T20)), implies(S20, implies(implies(T20, W20), implies(U20, W20))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19)))), implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(W19, V19), implies(V19, implies(W19, V19)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true, is_a_theorem(implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(W19, V19)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.11/8.66 = { by axiom 1 (ifeq_axiom) R->L }
% 39.11/8.66 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W20, V20), implies(U20, T20)), implies(S20, implies(implies(T20, W20), implies(U20, W20))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19)))), implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(W19, V19), implies(V19, implies(W19, V19)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true, is_a_theorem(implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(W19, V19)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.11/8.66 = { by axiom 2 (condensed_detachment) R->L }
% 39.11/8.67 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(V19, implies(Z20, V19))), implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))))), implies(implies(implies(implies(W20, V20), implies(U20, T20)), implies(S20, implies(implies(T20, W20), implies(U20, W20)))), implies(implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19)))), implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(W19, V19), implies(V19, implies(W19, V19)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(V19, implies(Z20, V19))), implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19)))))), true, is_a_theorem(implies(implies(implies(implies(W20, V20), implies(U20, T20)), implies(S20, implies(implies(T20, W20), implies(U20, W20)))), implies(implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19)))), implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W20, V20), implies(U20, T20)), implies(S20, implies(implies(T20, W20), implies(U20, W20))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19)))), implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(W19, V19), implies(V19, implies(W19, V19)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true, is_a_theorem(implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(W19, V19)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.11/8.67 = { by axiom 3 (ic_JLukasiewicz_4) }
% 39.11/8.68 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(V19, implies(Z20, V19))), implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19)))))), true, is_a_theorem(implies(implies(implies(implies(W20, V20), implies(U20, T20)), implies(S20, implies(implies(T20, W20), implies(U20, W20)))), implies(implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19)))), implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W20, V20), implies(U20, T20)), implies(S20, implies(implies(T20, W20), implies(U20, W20))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19)))), implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(W19, V19), implies(V19, implies(W19, V19)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true, is_a_theorem(implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(W19, V19)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.11/8.68 = { by axiom 1 (ifeq_axiom) }
% 39.11/8.68 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(V19, implies(Z20, V19))), implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19)))))), true, is_a_theorem(implies(implies(implies(implies(W20, V20), implies(U20, T20)), implies(S20, implies(implies(T20, W20), implies(U20, W20)))), implies(implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19)))), implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W20, V20), implies(U20, T20)), implies(S20, implies(implies(T20, W20), implies(U20, W20))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19)))), implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(W19, V19), implies(V19, implies(W19, V19)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true, is_a_theorem(implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(W19, V19)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.11/8.69 = { by axiom 3 (ic_JLukasiewicz_4) }
% 39.11/8.69 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W20, V20), implies(U20, T20)), implies(S20, implies(implies(T20, W20), implies(U20, W20)))), implies(implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19)))), implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W20, V20), implies(U20, T20)), implies(S20, implies(implies(T20, W20), implies(U20, W20))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19)))), implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(W19, V19), implies(V19, implies(W19, V19)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true, is_a_theorem(implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(W19, V19)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.11/8.69 = { by axiom 1 (ifeq_axiom) }
% 39.11/8.70 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W20, V20), implies(U20, T20)), implies(S20, implies(implies(T20, W20), implies(U20, W20)))), implies(implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19)))), implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))))), true, ifeq(is_a_theorem(implies(implies(implies(W20, V20), implies(U20, T20)), implies(S20, implies(implies(T20, W20), implies(U20, W20))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19)))), implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(W19, V19), implies(V19, implies(W19, V19)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true, is_a_theorem(implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(W19, V19)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.31/8.70 = { by axiom 2 (condensed_detachment) }
% 39.31/8.70 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true, is_a_theorem(implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(W19, V19)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.31/8.70 = { by axiom 1 (ifeq_axiom) }
% 39.31/8.71 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true, is_a_theorem(implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(W19, V19)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.31/8.71 = { by axiom 1 (ifeq_axiom) R->L }
% 39.31/8.71 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true), true, is_a_theorem(implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(W19, V19)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.31/8.72 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 39.31/8.72 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X21, Y21), implies(Z21, W21)), implies(V21, implies(implies(W21, X21), implies(Z21, X21))))), true, is_a_theorem(implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true), true, is_a_theorem(implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(W19, V19)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.31/8.73 = { by axiom 1 (ifeq_axiom) R->L }
% 39.31/8.74 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X21, Y21), implies(Z21, W21)), implies(V21, implies(implies(W21, X21), implies(Z21, X21))))), true, is_a_theorem(implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(W19, V19)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.31/8.74 = { by axiom 2 (condensed_detachment) R->L }
% 39.31/8.74 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V19, implies(W19, V19)), implies(W19, Z20)), implies(implies(W19, V19), implies(implies(Z20, V19), implies(W19, V19)))), implies(implies(implies(implies(X21, Y21), implies(Z21, W21)), implies(V21, implies(implies(W21, X21), implies(Z21, X21)))), implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))))), true, ifeq(is_a_theorem(implies(implies(implies(V19, implies(W19, V19)), implies(W19, Z20)), implies(implies(W19, V19), implies(implies(Z20, V19), implies(W19, V19))))), true, is_a_theorem(implies(implies(implies(implies(X21, Y21), implies(Z21, W21)), implies(V21, implies(implies(W21, X21), implies(Z21, X21)))), implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X21, Y21), implies(Z21, W21)), implies(V21, implies(implies(W21, X21), implies(Z21, X21))))), true, is_a_theorem(implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(W19, V19)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.31/8.75 = { by axiom 3 (ic_JLukasiewicz_4) }
% 39.31/8.75 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V19, implies(W19, V19)), implies(W19, Z20)), implies(implies(W19, V19), implies(implies(Z20, V19), implies(W19, V19))))), true, is_a_theorem(implies(implies(implies(implies(X21, Y21), implies(Z21, W21)), implies(V21, implies(implies(W21, X21), implies(Z21, X21)))), implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X21, Y21), implies(Z21, W21)), implies(V21, implies(implies(W21, X21), implies(Z21, X21))))), true, is_a_theorem(implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(W19, V19)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.31/8.75 = { by axiom 1 (ifeq_axiom) }
% 39.31/8.76 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V19, implies(W19, V19)), implies(W19, Z20)), implies(implies(W19, V19), implies(implies(Z20, V19), implies(W19, V19))))), true, is_a_theorem(implies(implies(implies(implies(X21, Y21), implies(Z21, W21)), implies(V21, implies(implies(W21, X21), implies(Z21, X21)))), implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X21, Y21), implies(Z21, W21)), implies(V21, implies(implies(W21, X21), implies(Z21, X21))))), true, is_a_theorem(implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(W19, V19)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.31/8.76 = { by axiom 3 (ic_JLukasiewicz_4) }
% 39.31/8.76 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X21, Y21), implies(Z21, W21)), implies(V21, implies(implies(W21, X21), implies(Z21, X21)))), implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X21, Y21), implies(Z21, W21)), implies(V21, implies(implies(W21, X21), implies(Z21, X21))))), true, is_a_theorem(implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(W19, V19)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.31/8.77 = { by axiom 1 (ifeq_axiom) }
% 39.31/8.77 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X21, Y21), implies(Z21, W21)), implies(V21, implies(implies(W21, X21), implies(Z21, X21)))), implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19)))))), true, ifeq(is_a_theorem(implies(implies(implies(X21, Y21), implies(Z21, W21)), implies(V21, implies(implies(W21, X21), implies(Z21, X21))))), true, is_a_theorem(implies(implies(implies(implies(Z20, V19), implies(W19, V19)), implies(V19, implies(W19, V19))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(W19, V19)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.31/8.77 = { by axiom 2 (condensed_detachment) }
% 39.31/8.77 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(W19, V19)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.31/8.77 = { by axiom 1 (ifeq_axiom) }
% 39.31/8.78 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(W19, V19), implies(V19, implies(W19, V19))))), true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(W19, V19)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.31/8.78 = { by axiom 2 (condensed_detachment) }
% 39.31/8.78 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.31/8.79 = { by axiom 1 (ifeq_axiom) }
% 39.31/8.79 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.31/8.79 = { by axiom 1 (ifeq_axiom) R->L }
% 39.31/8.79 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.52/8.80 = { by axiom 2 (condensed_detachment) R->L }
% 39.52/8.80 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, ifeq(is_a_theorem(implies(implies(U21, T21), implies(T21, implies(U21, T21)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.52/8.81 = { by axiom 1 (ifeq_axiom) R->L }
% 39.52/8.81 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(U21, T21), implies(T21, implies(U21, T21)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.52/8.82 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 39.52/8.82 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21))))), true, is_a_theorem(implies(implies(U21, T21), implies(T21, implies(U21, T21)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.52/8.83 = { by axiom 1 (ifeq_axiom) R->L }
% 39.52/8.83 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21))))), true, is_a_theorem(implies(implies(U21, T21), implies(T21, implies(U21, T21)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.52/8.84 = { by axiom 2 (condensed_detachment) R->L }
% 39.52/8.84 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21)))), implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(U21, T21), implies(T21, implies(U21, T21)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true, is_a_theorem(implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21))))), true, is_a_theorem(implies(implies(U21, T21), implies(T21, implies(U21, T21)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.52/8.85 = { by axiom 1 (ifeq_axiom) R->L }
% 39.52/8.85 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21)))), implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(U21, T21), implies(T21, implies(U21, T21)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true, is_a_theorem(implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21))))), true, is_a_theorem(implies(implies(U21, T21), implies(T21, implies(U21, T21)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.52/8.86 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 39.52/8.87 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U22, T22), implies(S22, X23)), implies(Y23, implies(implies(X23, U22), implies(S22, U22))))), true, is_a_theorem(implies(implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21)))), implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(U21, T21), implies(T21, implies(U21, T21)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true, is_a_theorem(implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21))))), true, is_a_theorem(implies(implies(U21, T21), implies(T21, implies(U21, T21)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.52/8.87 = { by axiom 1 (ifeq_axiom) R->L }
% 39.52/8.88 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U22, T22), implies(S22, X23)), implies(Y23, implies(implies(X23, U22), implies(S22, U22))))), true, is_a_theorem(implies(implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21)))), implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(U21, T21), implies(T21, implies(U21, T21)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true, is_a_theorem(implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21))))), true, is_a_theorem(implies(implies(U21, T21), implies(T21, implies(U21, T21)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.52/8.88 = { by axiom 2 (condensed_detachment) R->L }
% 39.52/8.89 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(T21, implies(V22, T21))), implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))))), implies(implies(implies(implies(U22, T22), implies(S22, X23)), implies(Y23, implies(implies(X23, U22), implies(S22, U22)))), implies(implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21)))), implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(U21, T21), implies(T21, implies(U21, T21)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(T21, implies(V22, T21))), implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21)))))), true, is_a_theorem(implies(implies(implies(implies(U22, T22), implies(S22, X23)), implies(Y23, implies(implies(X23, U22), implies(S22, U22)))), implies(implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21)))), implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U22, T22), implies(S22, X23)), implies(Y23, implies(implies(X23, U22), implies(S22, U22))))), true, is_a_theorem(implies(implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21)))), implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(U21, T21), implies(T21, implies(U21, T21)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true, is_a_theorem(implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21))))), true, is_a_theorem(implies(implies(U21, T21), implies(T21, implies(U21, T21)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.52/8.90 = { by axiom 3 (ic_JLukasiewicz_4) }
% 39.72/8.90 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(T21, implies(V22, T21))), implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21)))))), true, is_a_theorem(implies(implies(implies(implies(U22, T22), implies(S22, X23)), implies(Y23, implies(implies(X23, U22), implies(S22, U22)))), implies(implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21)))), implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U22, T22), implies(S22, X23)), implies(Y23, implies(implies(X23, U22), implies(S22, U22))))), true, is_a_theorem(implies(implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21)))), implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(U21, T21), implies(T21, implies(U21, T21)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true, is_a_theorem(implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21))))), true, is_a_theorem(implies(implies(U21, T21), implies(T21, implies(U21, T21)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.72/8.91 = { by axiom 1 (ifeq_axiom) }
% 39.72/8.92 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(T21, implies(V22, T21))), implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21)))))), true, is_a_theorem(implies(implies(implies(implies(U22, T22), implies(S22, X23)), implies(Y23, implies(implies(X23, U22), implies(S22, U22)))), implies(implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21)))), implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U22, T22), implies(S22, X23)), implies(Y23, implies(implies(X23, U22), implies(S22, U22))))), true, is_a_theorem(implies(implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21)))), implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(U21, T21), implies(T21, implies(U21, T21)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true, is_a_theorem(implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21))))), true, is_a_theorem(implies(implies(U21, T21), implies(T21, implies(U21, T21)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.72/8.92 = { by axiom 3 (ic_JLukasiewicz_4) }
% 39.72/8.93 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U22, T22), implies(S22, X23)), implies(Y23, implies(implies(X23, U22), implies(S22, U22)))), implies(implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21)))), implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U22, T22), implies(S22, X23)), implies(Y23, implies(implies(X23, U22), implies(S22, U22))))), true, is_a_theorem(implies(implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21)))), implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(U21, T21), implies(T21, implies(U21, T21)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true, is_a_theorem(implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21))))), true, is_a_theorem(implies(implies(U21, T21), implies(T21, implies(U21, T21)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.72/8.93 = { by axiom 1 (ifeq_axiom) }
% 39.72/8.94 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U22, T22), implies(S22, X23)), implies(Y23, implies(implies(X23, U22), implies(S22, U22)))), implies(implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21)))), implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))))), true, ifeq(is_a_theorem(implies(implies(implies(U22, T22), implies(S22, X23)), implies(Y23, implies(implies(X23, U22), implies(S22, U22))))), true, is_a_theorem(implies(implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21)))), implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(U21, T21), implies(T21, implies(U21, T21)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true, is_a_theorem(implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21))))), true, is_a_theorem(implies(implies(U21, T21), implies(T21, implies(U21, T21)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.72/8.94 = { by axiom 2 (condensed_detachment) }
% 39.72/8.95 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true, is_a_theorem(implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21))))), true, is_a_theorem(implies(implies(U21, T21), implies(T21, implies(U21, T21)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.72/8.95 = { by axiom 1 (ifeq_axiom) }
% 39.72/8.96 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true, is_a_theorem(implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21))))), true, is_a_theorem(implies(implies(U21, T21), implies(T21, implies(U21, T21)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.72/8.96 = { by axiom 1 (ifeq_axiom) R->L }
% 39.72/8.97 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true), true, is_a_theorem(implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21))))), true, is_a_theorem(implies(implies(U21, T21), implies(T21, implies(U21, T21)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.72/8.97 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 39.72/8.98 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z23, W23), implies(V23, U23)), implies(T23, implies(implies(U23, Z23), implies(V23, Z23))))), true, is_a_theorem(implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true), true, is_a_theorem(implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21))))), true, is_a_theorem(implies(implies(U21, T21), implies(T21, implies(U21, T21)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.72/8.98 = { by axiom 1 (ifeq_axiom) R->L }
% 39.72/8.99 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Z23, W23), implies(V23, U23)), implies(T23, implies(implies(U23, Z23), implies(V23, Z23))))), true, is_a_theorem(implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21))))), true, is_a_theorem(implies(implies(U21, T21), implies(T21, implies(U21, T21)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.72/8.99 = { by axiom 2 (condensed_detachment) R->L }
% 39.72/9.00 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T21, implies(U21, T21)), implies(U21, V22)), implies(implies(U21, T21), implies(implies(V22, T21), implies(U21, T21)))), implies(implies(implies(implies(Z23, W23), implies(V23, U23)), implies(T23, implies(implies(U23, Z23), implies(V23, Z23)))), implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))))), true, ifeq(is_a_theorem(implies(implies(implies(T21, implies(U21, T21)), implies(U21, V22)), implies(implies(U21, T21), implies(implies(V22, T21), implies(U21, T21))))), true, is_a_theorem(implies(implies(implies(implies(Z23, W23), implies(V23, U23)), implies(T23, implies(implies(U23, Z23), implies(V23, Z23)))), implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z23, W23), implies(V23, U23)), implies(T23, implies(implies(U23, Z23), implies(V23, Z23))))), true, is_a_theorem(implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21))))), true, is_a_theorem(implies(implies(U21, T21), implies(T21, implies(U21, T21)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.72/9.01 = { by axiom 3 (ic_JLukasiewicz_4) }
% 39.72/9.01 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T21, implies(U21, T21)), implies(U21, V22)), implies(implies(U21, T21), implies(implies(V22, T21), implies(U21, T21))))), true, is_a_theorem(implies(implies(implies(implies(Z23, W23), implies(V23, U23)), implies(T23, implies(implies(U23, Z23), implies(V23, Z23)))), implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z23, W23), implies(V23, U23)), implies(T23, implies(implies(U23, Z23), implies(V23, Z23))))), true, is_a_theorem(implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21))))), true, is_a_theorem(implies(implies(U21, T21), implies(T21, implies(U21, T21)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.72/9.02 = { by axiom 1 (ifeq_axiom) }
% 39.72/9.02 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T21, implies(U21, T21)), implies(U21, V22)), implies(implies(U21, T21), implies(implies(V22, T21), implies(U21, T21))))), true, is_a_theorem(implies(implies(implies(implies(Z23, W23), implies(V23, U23)), implies(T23, implies(implies(U23, Z23), implies(V23, Z23)))), implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z23, W23), implies(V23, U23)), implies(T23, implies(implies(U23, Z23), implies(V23, Z23))))), true, is_a_theorem(implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21))))), true, is_a_theorem(implies(implies(U21, T21), implies(T21, implies(U21, T21)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 39.72/9.03 = { by axiom 3 (ic_JLukasiewicz_4) }
% 40.00/9.03 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z23, W23), implies(V23, U23)), implies(T23, implies(implies(U23, Z23), implies(V23, Z23)))), implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z23, W23), implies(V23, U23)), implies(T23, implies(implies(U23, Z23), implies(V23, Z23))))), true, is_a_theorem(implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21))))), true, is_a_theorem(implies(implies(U21, T21), implies(T21, implies(U21, T21)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 40.00/9.04 = { by axiom 1 (ifeq_axiom) }
% 40.00/9.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z23, W23), implies(V23, U23)), implies(T23, implies(implies(U23, Z23), implies(V23, Z23)))), implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21)))))), true, ifeq(is_a_theorem(implies(implies(implies(Z23, W23), implies(V23, U23)), implies(T23, implies(implies(U23, Z23), implies(V23, Z23))))), true, is_a_theorem(implies(implies(implies(implies(V22, T21), implies(U21, T21)), implies(T21, implies(U21, T21))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21))))), true, is_a_theorem(implies(implies(U21, T21), implies(T21, implies(U21, T21)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 40.00/9.05 = { by axiom 2 (condensed_detachment) }
% 40.00/9.05 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21))))), true, is_a_theorem(implies(implies(U21, T21), implies(T21, implies(U21, T21)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 40.00/9.05 = { by axiom 1 (ifeq_axiom) }
% 40.00/9.06 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21)))), implies(implies(U21, T21), implies(T21, implies(U21, T21))))), true, ifeq(is_a_theorem(implies(implies(implies(S21, X22), implies(Y22, Z22)), implies(W22, implies(implies(Z22, S21), implies(Y22, S21))))), true, is_a_theorem(implies(implies(U21, T21), implies(T21, implies(U21, T21)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 40.00/9.06 = { by axiom 2 (condensed_detachment) }
% 40.00/9.06 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 40.00/9.07 = { by axiom 1 (ifeq_axiom) }
% 40.00/9.07 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 40.00/9.08 = { by axiom 1 (ifeq_axiom) R->L }
% 40.00/9.08 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 40.00/9.09 = { by axiom 2 (condensed_detachment) R->L }
% 40.00/9.10 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, ifeq(is_a_theorem(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 40.00/9.11 = { by axiom 1 (ifeq_axiom) R->L }
% 40.00/9.11 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 40.00/9.13 = { by axiom 2 (condensed_detachment) R->L }
% 40.20/9.13 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V24, U24), implies(T24, S24)), implies(X25, implies(implies(S24, V24), implies(T24, V24)))), implies(implies(implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))))), true, ifeq(is_a_theorem(implies(implies(implies(V24, U24), implies(T24, S24)), implies(X25, implies(implies(S24, V24), implies(T24, V24))))), true, is_a_theorem(implies(implies(implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 40.20/9.15 = { by axiom 1 (ifeq_axiom) R->L }
% 40.20/9.16 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V24, U24), implies(T24, S24)), implies(X25, implies(implies(S24, V24), implies(T24, V24)))), implies(implies(implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V24, U24), implies(T24, S24)), implies(X25, implies(implies(S24, V24), implies(T24, V24))))), true, is_a_theorem(implies(implies(implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 40.20/9.17 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 40.20/9.19 ifeq(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(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), Y25)), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(V24, U24), implies(T24, S24)), implies(X25, implies(implies(S24, V24), implies(T24, V24)))), implies(implies(implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V24, U24), implies(T24, S24)), implies(X25, implies(implies(S24, V24), implies(T24, V24))))), true, is_a_theorem(implies(implies(implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 40.20/9.20 = { by axiom 1 (ifeq_axiom) R->L }
% 40.34/9.22 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), Y25)), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(V24, U24), implies(T24, S24)), implies(X25, implies(implies(S24, V24), implies(T24, V24)))), implies(implies(implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, 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% 40.34/9.22 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
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implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 40.34/9.25 = { by axiom 2 (condensed_detachment) }
% 40.34/9.25 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V24, U24), implies(T24, S24)), implies(X25, implies(implies(S24, V24), implies(T24, V24))))), true, is_a_theorem(implies(implies(implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 40.34/9.26 = { by axiom 1 (ifeq_axiom) }
% 40.34/9.27 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V24, U24), implies(T24, S24)), implies(X25, implies(implies(S24, V24), implies(T24, V24))))), true, is_a_theorem(implies(implies(implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 40.34/9.28 = { by axiom 3 (ic_JLukasiewicz_4) }
% 40.34/9.29 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 40.54/9.30 = { by axiom 1 (ifeq_axiom) }
% 40.54/9.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 40.54/9.33 = { by axiom 1 (ifeq_axiom) R->L }
% 40.54/9.33 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 40.54/9.35 = { by axiom 2 (condensed_detachment) R->L }
% 40.54/9.36 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z25, W25), implies(V25, U25)), implies(T25, implies(implies(U25, Z25), implies(V25, Z25)))), implies(implies(implies(implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))))), true, ifeq(is_a_theorem(implies(implies(implies(Z25, W25), implies(V25, U25)), implies(T25, implies(implies(U25, Z25), implies(V25, Z25))))), true, is_a_theorem(implies(implies(implies(implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, 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% 40.54/9.38 = { by axiom 1 (ifeq_axiom) R->L }
% 40.54/9.40 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z25, W25), implies(V25, U25)), implies(T25, implies(implies(U25, Z25), implies(V25, Z25)))), implies(implies(implies(implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), 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implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 40.74/9.42 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 40.74/9.43 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))))), true, is_a_theorem(implies(implies(implies(implies(Z25, W25), implies(V25, U25)), implies(T25, implies(implies(U25, Z25), implies(V25, Z25)))), implies(implies(implies(implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z25, W25), implies(V25, U25)), implies(T25, implies(implies(U25, Z25), implies(V25, Z25))))), true, is_a_theorem(implies(implies(implies(implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 40.74/9.45 = { by axiom 1 (ifeq_axiom) R->L }
% 40.74/9.46 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))))), true, is_a_theorem(implies(implies(implies(implies(Z25, W25), implies(V25, U25)), implies(T25, implies(implies(U25, Z25), implies(V25, Z25)))), implies(implies(implies(implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z25, W25), implies(V25, U25)), implies(T25, implies(implies(U25, Z25), implies(V25, Z25))))), true, is_a_theorem(implies(implies(implies(implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 40.74/9.47 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 40.74/9.49 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), implies(implies(implies(implies(Z25, W25), implies(V25, U25)), implies(T25, implies(implies(U25, Z25), implies(V25, Z25)))), implies(implies(implies(implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X, Y), 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implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))))), true, is_a_theorem(implies(implies(implies(implies(Z25, W25), implies(V25, U25)), implies(T25, implies(implies(U25, Z25), implies(V25, Z25)))), implies(implies(implies(implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), 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implies(implies(a, b), b)), implies(implies(a, b), b)))))), implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z25, W25), implies(V25, U25)), implies(T25, implies(implies(U25, Z25), implies(V25, Z25))))), true, is_a_theorem(implies(implies(implies(implies(implies(Y25, 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% 40.95/9.50 = { by axiom 2 (condensed_detachment) }
% 40.95/9.51 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Z25, W25), implies(V25, U25)), implies(T25, implies(implies(U25, Z25), implies(V25, Z25))))), true, is_a_theorem(implies(implies(implies(implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), 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implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 40.95/9.52 = { by axiom 1 (ifeq_axiom) }
% 40.95/9.53 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z25, W25), implies(V25, U25)), implies(T25, implies(implies(U25, Z25), implies(V25, Z25))))), true, is_a_theorem(implies(implies(implies(implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 40.95/9.53 = { by axiom 3 (ic_JLukasiewicz_4) }
% 40.95/9.54 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 40.95/9.55 = { by axiom 1 (ifeq_axiom) }
% 40.95/9.56 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y25, implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 40.95/9.56 = { by axiom 2 (condensed_detachment) }
% 40.95/9.57 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 40.95/9.57 = { by axiom 1 (ifeq_axiom) }
% 40.95/9.58 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 40.95/9.58 = { by axiom 3 (ic_JLukasiewicz_4) }
% 40.95/9.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 40.95/9.59 = { by axiom 1 (ifeq_axiom) }
% 40.95/9.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 40.95/9.60 = { by axiom 1 (ifeq_axiom) R->L }
% 41.16/9.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 41.16/9.60 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 41.16/9.61 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(U21, T21), implies(T21, implies(U21, T21))), implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 41.16/9.61 = { by axiom 2 (condensed_detachment) }
% 41.16/9.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 41.16/9.62 = { by axiom 1 (ifeq_axiom) }
% 41.16/9.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 41.16/9.63 = { by axiom 1 (ifeq_axiom) R->L }
% 41.16/9.63 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 41.16/9.64 = { by axiom 2 (condensed_detachment) R->L }
% 41.16/9.64 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S25, X26), implies(Y26, Z26)), implies(W26, implies(implies(Z26, S25), implies(Y26, S25)))), implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))))), true, ifeq(is_a_theorem(implies(implies(implies(S25, X26), implies(Y26, Z26)), implies(W26, implies(implies(Z26, S25), implies(Y26, S25))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 41.16/9.65 = { by axiom 1 (ifeq_axiom) R->L }
% 41.16/9.66 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S25, X26), implies(Y26, Z26)), implies(W26, implies(implies(Z26, S25), implies(Y26, S25)))), implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S25, X26), implies(Y26, Z26)), implies(W26, implies(implies(Z26, S25), implies(Y26, S25))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 41.16/9.66 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 41.16/9.67 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(S25, X26), implies(Y26, Z26)), implies(W26, implies(implies(Z26, S25), implies(Y26, S25)))), implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S25, X26), implies(Y26, Z26)), implies(W26, implies(implies(Z26, S25), implies(Y26, S25))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 41.16/9.67 = { by axiom 1 (ifeq_axiom) R->L }
% 41.16/9.68 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(S25, X26), implies(Y26, Z26)), implies(W26, implies(implies(Z26, S25), implies(Y26, S25)))), implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S25, X26), implies(Y26, Z26)), implies(W26, implies(implies(Z26, S25), implies(Y26, S25))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 41.16/9.68 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 41.16/9.69 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), implies(implies(implies(implies(S25, X26), implies(Y26, Z26)), implies(W26, implies(implies(Z26, S25), implies(Y26, S25)))), implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(S25, X26), implies(Y26, Z26)), implies(W26, implies(implies(Z26, S25), implies(Y26, S25)))), implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S25, X26), implies(Y26, Z26)), implies(W26, implies(implies(Z26, S25), implies(Y26, S25))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 41.16/9.70 = { by axiom 2 (condensed_detachment) }
% 41.36/9.70 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(S25, X26), implies(Y26, Z26)), implies(W26, implies(implies(Z26, S25), implies(Y26, S25))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 41.36/9.70 = { by axiom 1 (ifeq_axiom) }
% 41.36/9.71 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S25, X26), implies(Y26, Z26)), implies(W26, implies(implies(Z26, S25), implies(Y26, S25))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 41.36/9.71 = { by axiom 3 (ic_JLukasiewicz_4) }
% 41.36/9.71 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 41.36/9.72 = { by axiom 1 (ifeq_axiom) }
% 41.36/9.72 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(W19, V19))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 41.36/9.72 = { by axiom 2 (condensed_detachment) }
% 41.36/9.72 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 41.36/9.72 = { by axiom 1 (ifeq_axiom) }
% 41.36/9.72 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 41.36/9.73 = { by axiom 1 (ifeq_axiom) R->L }
% 41.36/9.73 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 41.36/9.73 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 41.36/9.73 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(Y17, Z17), implies(Z17, implies(Y17, Z17))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 41.36/9.73 = { by axiom 2 (condensed_detachment) }
% 41.36/9.73 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 41.36/9.73 = { by axiom 1 (ifeq_axiom) }
% 41.36/9.74 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 41.36/9.74 = { by axiom 1 (ifeq_axiom) R->L }
% 41.36/9.74 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 41.36/9.74 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 41.36/9.74 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(a, b), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(S14, X15), implies(X15, implies(S14, X15))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 41.36/9.74 = { by axiom 2 (condensed_detachment) }
% 41.36/9.74 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 41.36/9.74 = { by axiom 1 (ifeq_axiom) }
% 41.36/9.74 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 41.36/9.74 = { by axiom 2 (condensed_detachment) }
% 41.36/9.74 ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 41.36/9.74 = { by axiom 1 (ifeq_axiom) }
% 41.36/9.74 ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 41.36/9.74 = { by axiom 1 (ifeq_axiom) R->L }
% 41.36/9.74 ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.36/9.74 = { by axiom 2 (condensed_detachment) R->L }
% 41.36/9.74 ifeq(ifeq(is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, ifeq(is_a_theorem(implies(implies(V26, U26), implies(U26, implies(V26, U26)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.36/9.74 = { by axiom 1 (ifeq_axiom) R->L }
% 41.36/9.74 ifeq(ifeq(is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(V26, U26), implies(U26, implies(V26, U26)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.36/9.74 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 41.36/9.74 ifeq(ifeq(is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26))))), true, is_a_theorem(implies(implies(V26, U26), implies(U26, implies(V26, U26)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.36/9.75 = { by axiom 1 (ifeq_axiom) R->L }
% 41.36/9.75 ifeq(ifeq(is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26))))), true, is_a_theorem(implies(implies(V26, U26), implies(U26, implies(V26, U26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.36/9.75 = { by axiom 2 (condensed_detachment) R->L }
% 41.36/9.75 ifeq(ifeq(is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26)))), implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(V26, U26), implies(U26, implies(V26, U26)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true, is_a_theorem(implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26))))), true, is_a_theorem(implies(implies(V26, U26), implies(U26, implies(V26, U26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.36/9.75 = { by axiom 1 (ifeq_axiom) R->L }
% 41.36/9.75 ifeq(ifeq(is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26)))), implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(V26, U26), implies(U26, implies(V26, U26)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true, is_a_theorem(implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26))))), true, is_a_theorem(implies(implies(V26, U26), implies(U26, implies(V26, U26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.36/9.75 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 41.36/9.75 ifeq(ifeq(is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V27, U27), implies(T27, S27)), implies(X28, implies(implies(S27, V27), implies(T27, V27))))), true, is_a_theorem(implies(implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26)))), implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(V26, U26), implies(U26, implies(V26, U26)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true, is_a_theorem(implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26))))), true, is_a_theorem(implies(implies(V26, U26), implies(U26, implies(V26, U26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.36/9.75 = { by axiom 1 (ifeq_axiom) R->L }
% 41.36/9.76 ifeq(ifeq(is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V27, U27), implies(T27, S27)), implies(X28, implies(implies(S27, V27), implies(T27, V27))))), true, is_a_theorem(implies(implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26)))), implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(V26, U26), implies(U26, implies(V26, U26)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true, is_a_theorem(implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26))))), true, is_a_theorem(implies(implies(V26, U26), implies(U26, implies(V26, U26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.36/9.76 = { by axiom 2 (condensed_detachment) R->L }
% 41.36/9.76 ifeq(ifeq(is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(U26, implies(W27, U26))), implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))))), implies(implies(implies(implies(V27, U27), implies(T27, S27)), implies(X28, implies(implies(S27, V27), implies(T27, V27)))), implies(implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26)))), implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(V26, U26), implies(U26, implies(V26, U26)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(U26, implies(W27, U26))), implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26)))))), true, is_a_theorem(implies(implies(implies(implies(V27, U27), implies(T27, S27)), implies(X28, implies(implies(S27, V27), implies(T27, V27)))), implies(implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26)))), implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V27, U27), implies(T27, S27)), implies(X28, implies(implies(S27, V27), implies(T27, V27))))), true, is_a_theorem(implies(implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26)))), implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(V26, U26), implies(U26, implies(V26, U26)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true, is_a_theorem(implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26))))), true, is_a_theorem(implies(implies(V26, U26), implies(U26, implies(V26, U26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.36/9.76 = { by axiom 3 (ic_JLukasiewicz_4) }
% 41.36/9.76 ifeq(ifeq(is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(U26, implies(W27, U26))), implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26)))))), true, is_a_theorem(implies(implies(implies(implies(V27, U27), implies(T27, S27)), implies(X28, implies(implies(S27, V27), implies(T27, V27)))), implies(implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26)))), implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V27, U27), implies(T27, S27)), implies(X28, implies(implies(S27, V27), implies(T27, V27))))), true, is_a_theorem(implies(implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26)))), implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(V26, U26), implies(U26, implies(V26, U26)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true, is_a_theorem(implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26))))), true, is_a_theorem(implies(implies(V26, U26), implies(U26, implies(V26, U26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.36/9.76 = { by axiom 1 (ifeq_axiom) }
% 41.36/9.77 ifeq(ifeq(is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(U26, implies(W27, U26))), implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26)))))), true, is_a_theorem(implies(implies(implies(implies(V27, U27), implies(T27, S27)), implies(X28, implies(implies(S27, V27), implies(T27, V27)))), implies(implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26)))), implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V27, U27), implies(T27, S27)), implies(X28, implies(implies(S27, V27), implies(T27, V27))))), true, is_a_theorem(implies(implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26)))), implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(V26, U26), implies(U26, implies(V26, U26)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true, is_a_theorem(implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26))))), true, is_a_theorem(implies(implies(V26, U26), implies(U26, implies(V26, U26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.36/9.77 = { by axiom 3 (ic_JLukasiewicz_4) }
% 41.36/9.77 ifeq(ifeq(is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V27, U27), implies(T27, S27)), implies(X28, implies(implies(S27, V27), implies(T27, V27)))), implies(implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26)))), implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V27, U27), implies(T27, S27)), implies(X28, implies(implies(S27, V27), implies(T27, V27))))), true, is_a_theorem(implies(implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26)))), implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(V26, U26), implies(U26, implies(V26, U26)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true, is_a_theorem(implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26))))), true, is_a_theorem(implies(implies(V26, U26), implies(U26, implies(V26, U26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.36/9.77 = { by axiom 1 (ifeq_axiom) }
% 41.36/9.77 ifeq(ifeq(is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V27, U27), implies(T27, S27)), implies(X28, implies(implies(S27, V27), implies(T27, V27)))), implies(implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26)))), implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))))), true, ifeq(is_a_theorem(implies(implies(implies(V27, U27), implies(T27, S27)), implies(X28, implies(implies(S27, V27), implies(T27, V27))))), true, is_a_theorem(implies(implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26)))), implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(V26, U26), implies(U26, implies(V26, U26)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true, is_a_theorem(implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26))))), true, is_a_theorem(implies(implies(V26, U26), implies(U26, implies(V26, U26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.36/9.77 = { by axiom 2 (condensed_detachment) }
% 41.36/9.77 ifeq(ifeq(is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true, is_a_theorem(implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26))))), true, is_a_theorem(implies(implies(V26, U26), implies(U26, implies(V26, U26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.36/9.77 = { by axiom 1 (ifeq_axiom) }
% 41.36/9.78 ifeq(ifeq(is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true, is_a_theorem(implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26))))), true, is_a_theorem(implies(implies(V26, U26), implies(U26, implies(V26, U26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.36/9.78 = { by axiom 1 (ifeq_axiom) R->L }
% 41.36/9.78 ifeq(ifeq(is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true), true, is_a_theorem(implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26))))), true, is_a_theorem(implies(implies(V26, U26), implies(U26, implies(V26, U26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.36/9.78 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 41.36/9.78 ifeq(ifeq(is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y28, Z28), implies(W28, V28)), implies(U28, implies(implies(V28, Y28), implies(W28, Y28))))), true, is_a_theorem(implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true), true, is_a_theorem(implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26))))), true, is_a_theorem(implies(implies(V26, U26), implies(U26, implies(V26, U26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.36/9.78 = { by axiom 1 (ifeq_axiom) R->L }
% 41.36/9.78 ifeq(ifeq(is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y28, Z28), implies(W28, V28)), implies(U28, implies(implies(V28, Y28), implies(W28, Y28))))), true, is_a_theorem(implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26))))), true, is_a_theorem(implies(implies(V26, U26), implies(U26, implies(V26, U26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.36/9.78 = { by axiom 2 (condensed_detachment) R->L }
% 41.36/9.78 ifeq(ifeq(is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U26, implies(V26, U26)), implies(V26, W27)), implies(implies(V26, U26), implies(implies(W27, U26), implies(V26, U26)))), implies(implies(implies(implies(Y28, Z28), implies(W28, V28)), implies(U28, implies(implies(V28, Y28), implies(W28, Y28)))), implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))))), true, ifeq(is_a_theorem(implies(implies(implies(U26, implies(V26, U26)), implies(V26, W27)), implies(implies(V26, U26), implies(implies(W27, U26), implies(V26, U26))))), true, is_a_theorem(implies(implies(implies(implies(Y28, Z28), implies(W28, V28)), implies(U28, implies(implies(V28, Y28), implies(W28, Y28)))), implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y28, Z28), implies(W28, V28)), implies(U28, implies(implies(V28, Y28), implies(W28, Y28))))), true, is_a_theorem(implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26))))), true, is_a_theorem(implies(implies(V26, U26), implies(U26, implies(V26, U26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.36/9.78 = { by axiom 3 (ic_JLukasiewicz_4) }
% 41.36/9.79 ifeq(ifeq(is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U26, implies(V26, U26)), implies(V26, W27)), implies(implies(V26, U26), implies(implies(W27, U26), implies(V26, U26))))), true, is_a_theorem(implies(implies(implies(implies(Y28, Z28), implies(W28, V28)), implies(U28, implies(implies(V28, Y28), implies(W28, Y28)))), implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y28, Z28), implies(W28, V28)), implies(U28, implies(implies(V28, Y28), implies(W28, Y28))))), true, is_a_theorem(implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26))))), true, is_a_theorem(implies(implies(V26, U26), implies(U26, implies(V26, U26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.36/9.79 = { by axiom 1 (ifeq_axiom) }
% 41.36/9.79 ifeq(ifeq(is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U26, implies(V26, U26)), implies(V26, W27)), implies(implies(V26, U26), implies(implies(W27, U26), implies(V26, U26))))), true, is_a_theorem(implies(implies(implies(implies(Y28, Z28), implies(W28, V28)), implies(U28, implies(implies(V28, Y28), implies(W28, Y28)))), implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y28, Z28), implies(W28, V28)), implies(U28, implies(implies(V28, Y28), implies(W28, Y28))))), true, is_a_theorem(implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26))))), true, is_a_theorem(implies(implies(V26, U26), implies(U26, implies(V26, U26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.36/9.79 = { by axiom 3 (ic_JLukasiewicz_4) }
% 41.36/9.79 ifeq(ifeq(is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y28, Z28), implies(W28, V28)), implies(U28, implies(implies(V28, Y28), implies(W28, Y28)))), implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y28, Z28), implies(W28, V28)), implies(U28, implies(implies(V28, Y28), implies(W28, Y28))))), true, is_a_theorem(implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26))))), true, is_a_theorem(implies(implies(V26, U26), implies(U26, implies(V26, U26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.36/9.79 = { by axiom 1 (ifeq_axiom) }
% 41.36/9.79 ifeq(ifeq(is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y28, Z28), implies(W28, V28)), implies(U28, implies(implies(V28, Y28), implies(W28, Y28)))), implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26)))))), true, ifeq(is_a_theorem(implies(implies(implies(Y28, Z28), implies(W28, V28)), implies(U28, implies(implies(V28, Y28), implies(W28, Y28))))), true, is_a_theorem(implies(implies(implies(implies(W27, U26), implies(V26, U26)), implies(U26, implies(V26, U26))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26))))), true, is_a_theorem(implies(implies(V26, U26), implies(U26, implies(V26, U26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.36/9.79 = { by axiom 2 (condensed_detachment) }
% 41.36/9.79 ifeq(ifeq(is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26))))), true, is_a_theorem(implies(implies(V26, U26), implies(U26, implies(V26, U26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.36/9.79 = { by axiom 1 (ifeq_axiom) }
% 41.36/9.79 ifeq(ifeq(is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26)))), implies(implies(V26, U26), implies(U26, implies(V26, U26))))), true, ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(X27, Y27)), implies(Z27, implies(implies(Y27, T26), implies(X27, T26))))), true, is_a_theorem(implies(implies(V26, U26), implies(U26, implies(V26, U26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.36/9.79 = { by axiom 2 (condensed_detachment) }
% 41.36/9.79 ifeq(ifeq(is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.36/9.79 = { by axiom 1 (ifeq_axiom) }
% 41.36/9.80 ifeq(ifeq(is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.36/9.80 = { by axiom 1 (ifeq_axiom) R->L }
% 41.36/9.80 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.36/9.80 = { by axiom 2 (condensed_detachment) R->L }
% 41.36/9.80 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(a, b), a)), implies(a, implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), b), T28), implies(a, implies(implies(a, b), implies(implies(a, b), b)))))), true, ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(a, b), a)), implies(a, implies(implies(a, b), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), T28), implies(a, implies(implies(a, b), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.58/9.80 = { by axiom 1 (ifeq_axiom) R->L }
% 41.58/9.80 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(a, b), a)), implies(a, implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), b), T28), implies(a, implies(implies(a, b), implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(a, b), a)), implies(a, implies(implies(a, b), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), T28), implies(a, implies(implies(a, b), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.58/9.80 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 41.58/9.80 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S28, X29), implies(Y29, Z29)), implies(W29, implies(implies(Z29, S28), implies(Y29, S28))))), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(a, b), a)), implies(a, implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), b), T28), implies(a, implies(implies(a, b), implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(a, b), a)), implies(a, implies(implies(a, b), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), T28), implies(a, implies(implies(a, b), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.58/9.80 = { by axiom 1 (ifeq_axiom) R->L }
% 41.58/9.80 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(S28, X29), implies(Y29, Z29)), implies(W29, implies(implies(Z29, S28), implies(Y29, S28))))), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(a, b), a)), implies(a, implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), b), T28), implies(a, implies(implies(a, b), implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(a, b), a)), implies(a, implies(implies(a, b), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), T28), implies(a, implies(implies(a, b), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.58/9.80 = { by axiom 2 (condensed_detachment) R->L }
% 41.58/9.81 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), T28), implies(implies(b, a), implies(implies(a, b), a)))), implies(implies(implies(implies(S28, X29), implies(Y29, Z29)), implies(W29, implies(implies(Z29, S28), implies(Y29, S28)))), implies(implies(implies(implies(b, a), implies(implies(a, b), a)), implies(a, implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), b), T28), implies(a, implies(implies(a, b), implies(implies(a, b), b)))))))), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), T28), implies(implies(b, a), implies(implies(a, b), a))))), true, is_a_theorem(implies(implies(implies(implies(S28, X29), implies(Y29, Z29)), implies(W29, implies(implies(Z29, S28), implies(Y29, S28)))), implies(implies(implies(implies(b, a), implies(implies(a, b), a)), implies(a, implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), b), T28), implies(a, implies(implies(a, b), implies(implies(a, b), b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S28, X29), implies(Y29, Z29)), implies(W29, implies(implies(Z29, S28), implies(Y29, S28))))), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(a, b), a)), implies(a, implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), b), T28), implies(a, implies(implies(a, b), implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(a, b), a)), implies(a, implies(implies(a, b), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), T28), implies(a, implies(implies(a, b), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.58/9.81 = { by axiom 3 (ic_JLukasiewicz_4) }
% 41.58/9.81 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), T28), implies(implies(b, a), implies(implies(a, b), a))))), true, is_a_theorem(implies(implies(implies(implies(S28, X29), implies(Y29, Z29)), implies(W29, implies(implies(Z29, S28), implies(Y29, S28)))), implies(implies(implies(implies(b, a), implies(implies(a, b), a)), implies(a, implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), b), T28), implies(a, implies(implies(a, b), implies(implies(a, b), b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S28, X29), implies(Y29, Z29)), implies(W29, implies(implies(Z29, S28), implies(Y29, S28))))), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(a, b), a)), implies(a, implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), b), T28), implies(a, implies(implies(a, b), implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(a, b), a)), implies(a, implies(implies(a, b), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), T28), implies(a, implies(implies(a, b), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.58/9.81 = { by axiom 1 (ifeq_axiom) }
% 41.58/9.81 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), T28), implies(implies(b, a), implies(implies(a, b), a))))), true, is_a_theorem(implies(implies(implies(implies(S28, X29), implies(Y29, Z29)), implies(W29, implies(implies(Z29, S28), implies(Y29, S28)))), implies(implies(implies(implies(b, a), implies(implies(a, b), a)), implies(a, implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), b), T28), implies(a, implies(implies(a, b), implies(implies(a, b), b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S28, X29), implies(Y29, Z29)), implies(W29, implies(implies(Z29, S28), implies(Y29, S28))))), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(a, b), a)), implies(a, implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), b), T28), implies(a, implies(implies(a, b), implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(a, b), a)), implies(a, implies(implies(a, b), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), T28), implies(a, implies(implies(a, b), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.58/9.81 = { by axiom 3 (ic_JLukasiewicz_4) }
% 41.58/9.81 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S28, X29), implies(Y29, Z29)), implies(W29, implies(implies(Z29, S28), implies(Y29, S28)))), implies(implies(implies(implies(b, a), implies(implies(a, b), a)), implies(a, implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), b), T28), implies(a, implies(implies(a, b), implies(implies(a, b), b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S28, X29), implies(Y29, Z29)), implies(W29, implies(implies(Z29, S28), implies(Y29, S28))))), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(a, b), a)), implies(a, implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), b), T28), implies(a, implies(implies(a, b), implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(a, b), a)), implies(a, implies(implies(a, b), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), T28), implies(a, implies(implies(a, b), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.58/9.81 = { by axiom 1 (ifeq_axiom) }
% 41.58/9.81 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S28, X29), implies(Y29, Z29)), implies(W29, implies(implies(Z29, S28), implies(Y29, S28)))), implies(implies(implies(implies(b, a), implies(implies(a, b), a)), implies(a, implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), b), T28), implies(a, implies(implies(a, b), implies(implies(a, b), b))))))), true, ifeq(is_a_theorem(implies(implies(implies(S28, X29), implies(Y29, Z29)), implies(W29, implies(implies(Z29, S28), implies(Y29, S28))))), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(a, b), a)), implies(a, implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), b), T28), implies(a, implies(implies(a, b), implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(a, b), a)), implies(a, implies(implies(a, b), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), T28), implies(a, implies(implies(a, b), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.58/9.81 = { by axiom 2 (condensed_detachment) }
% 41.58/9.82 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(a, b), a)), implies(a, implies(implies(a, b), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), T28), implies(a, implies(implies(a, b), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.58/9.82 = { by axiom 1 (ifeq_axiom) }
% 41.58/9.82 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(a, b), a)), implies(a, implies(implies(a, b), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), T28), implies(a, implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.58/9.82 = { by axiom 3 (ic_JLukasiewicz_4) }
% 41.58/9.82 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), b), T28), implies(a, implies(implies(a, b), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.58/9.82 = { by axiom 1 (ifeq_axiom) }
% 41.58/9.82 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), b), T28), implies(a, implies(implies(a, b), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.58/9.82 = { by axiom 1 (ifeq_axiom) R->L }
% 41.58/9.82 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), b), T28), implies(a, implies(implies(a, b), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.58/9.82 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 41.58/9.82 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), b), T28), implies(a, implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), b), T28), implies(a, implies(implies(a, b), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(V26, U26), implies(U26, implies(V26, U26))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.58/9.82 = { by axiom 2 (condensed_detachment) }
% 41.58/9.82 ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.58/9.82 = { by axiom 1 (ifeq_axiom) }
% 41.58/9.82 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 41.58/9.82 = { by axiom 2 (condensed_detachment) }
% 41.58/9.82 true
% 41.58/9.82 % SZS output end Proof
% 41.58/9.82
% 41.58/9.82 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------